KILLED proof of input_VrWUnExYid.trs # AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF).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), 5 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), 0 ms] (30) CdtProblem (31) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (32) CdtProblem (33) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (34) CdtProblem (35) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (36) CdtProblem (37) 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) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (44) CdtProblem (45) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (46) CdtProblem (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (48) CdtProblem (49) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (50) CdtProblem (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (52) CdtProblem (53) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (54) CdtProblem (55) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (56) CdtProblem (57) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (58) CdtProblem (59) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (60) CdtProblem (61) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (62) CdtProblem (63) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (64) CdtProblem (65) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (66) CdtProblem (67) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (68) CdtProblem (69) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (70) CdtProblem (71) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (72) CdtProblem (73) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (74) CdtProblem (75) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (76) CdtProblem (77) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 6 ms] (78) CdtProblem (79) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (80) CdtProblem (81) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 8 ms] (82) CdtProblem (83) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (84) CdtProblem (85) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (86) CdtProblem (87) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (88) CdtProblem (89) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (90) CdtProblem (91) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (92) CdtProblem (93) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (94) CdtProblem (95) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (96) CdtProblem (97) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (98) CdtProblem (99) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (100) CdtProblem (101) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 10 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), 0 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), 10 ms] (118) CdtProblem (119) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (120) CdtProblem (121) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (122) CdtProblem (123) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (124) CdtProblem (125) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (126) CdtProblem (127) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (128) CdtProblem (129) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (130) CdtProblem (131) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (132) CdtProblem (133) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (134) CdtProblem (135) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (136) CdtProblem (137) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (138) CdtProblem (139) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (140) CdtProblem (141) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (142) CdtProblem (143) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (144) CdtProblem (145) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 12 ms] (146) CdtProblem (147) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (148) CdtProblem (149) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (150) CdtProblem (151) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (152) CdtProblem (153) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 37 ms] (154) CdtProblem (155) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 10 ms] (156) CdtProblem (157) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 33 ms] (158) CdtProblem (159) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (160) CdtProblem (161) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 94 ms] (162) CdtProblem (163) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (164) CdtProblem (165) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 23 ms] (166) CdtProblem (167) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (168) CdtProblem (169) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 33 ms] (170) CdtProblem (171) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (172) CdtProblem (173) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 120 ms] (174) CdtProblem (175) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (176) CdtProblem (177) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 74 ms] (178) CdtProblem (179) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (180) CdtProblem (181) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (182) CdtProblem (183) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 3 ms] (184) CdtProblem (185) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 83 ms] (186) CdtProblem (187) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (188) CdtProblem (189) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 52 ms] (190) CdtProblem (191) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (192) CdtProblem (193) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (194) CdtProblem (195) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 19 ms] (196) CdtProblem (197) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 38 ms] (198) CdtProblem (199) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 9 ms] (200) CdtProblem (201) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 48 ms] (202) CdtProblem (203) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (204) CdtProblem (205) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 94 ms] (206) CdtProblem (207) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (208) CdtProblem (209) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 141 ms] (210) CdtProblem (211) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (212) CdtProblem (213) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 90 ms] (214) CdtProblem (215) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (216) CdtProblem (217) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (218) CdtProblem (219) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 160 ms] (220) CdtProblem (221) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 28 ms] (222) CdtProblem (223) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 2 ms] (224) CdtProblem (225) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 195 ms] (226) CdtProblem (227) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 7 ms] (228) CdtProblem (229) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 12 ms] (230) CdtProblem (231) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 61 ms] (232) CdtProblem (233) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (234) CdtProblem (235) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 1 ms] (236) CdtProblem ---------------------------------------- (0) Obligation: The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: a__U11(tt, M, N) -> a__U12(tt, M, N) a__U12(tt, M, N) -> s(a__plus(mark(N), mark(M))) a__plus(N, 0) -> mark(N) a__plus(N, s(M)) -> a__U11(tt, M, N) mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3) mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3) mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) mark(tt) -> tt mark(s(X)) -> s(mark(X)) mark(0) -> 0 a__U11(X1, X2, X3) -> U11(X1, X2, X3) a__U12(X1, X2, X3) -> U12(X1, X2, X3) 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__U11(tt, M, N) -> a__U12(tt, M, N) a__U12(tt, M, N) -> s(a__plus(mark(N), mark(M))) a__plus(N, 0') -> mark(N) a__plus(N, s(M)) -> a__U11(tt, M, N) mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3) mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3) mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) mark(tt) -> tt mark(s(X)) -> s(mark(X)) mark(0') -> 0' a__U11(X1, X2, X3) -> U11(X1, X2, X3) a__U12(X1, X2, X3) -> U12(X1, X2, X3) 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__U11(tt, M, N) -> a__U12(tt, M, N) a__U12(tt, M, N) -> s(a__plus(mark(N), mark(M))) a__plus(N, 0) -> mark(N) a__plus(N, s(M)) -> a__U11(tt, M, N) mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3) mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3) mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) mark(tt) -> tt mark(s(X)) -> s(mark(X)) mark(0) -> 0 a__U11(X1, X2, X3) -> U11(X1, X2, X3) a__U12(X1, X2, X3) -> U12(X1, X2, X3) 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__U11(tt, M, N) -> a__U12(tt, M, N) [1] a__U12(tt, M, N) -> s(a__plus(mark(N), mark(M))) [1] a__plus(N, 0) -> mark(N) [1] a__plus(N, s(M)) -> a__U11(tt, M, N) [1] mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3) [1] mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3) [1] mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) [1] mark(tt) -> tt [1] mark(s(X)) -> s(mark(X)) [1] mark(0) -> 0 [1] a__U11(X1, X2, X3) -> U11(X1, X2, X3) [1] a__U12(X1, X2, X3) -> U12(X1, X2, X3) [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__U11(tt, M, N) -> a__U12(tt, M, N) [1] a__U12(tt, M, N) -> s(a__plus(mark(N), mark(M))) [1] a__plus(N, 0) -> mark(N) [1] a__plus(N, s(M)) -> a__U11(tt, M, N) [1] mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3) [1] mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3) [1] mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) [1] mark(tt) -> tt [1] mark(s(X)) -> s(mark(X)) [1] mark(0) -> 0 [1] a__U11(X1, X2, X3) -> U11(X1, X2, X3) [1] a__U12(X1, X2, X3) -> U12(X1, X2, X3) [1] a__plus(X1, X2) -> plus(X1, X2) [1] The TRS has the following type information: a__U11 :: tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus tt :: tt:s:0:U11:U12:plus a__U12 :: tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus s :: tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus a__plus :: tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus mark :: tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus 0 :: tt:s:0:U11:U12:plus U11 :: tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus U12 :: tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus plus :: tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus -> tt:s:0:U11:U12: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__U12_3 a__U11_3 a__plus_2 Due to the following rules being added: none And the following fresh constants: none ---------------------------------------- (10) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__U11(tt, M, N) -> a__U12(tt, M, N) [1] a__U12(tt, M, N) -> s(a__plus(mark(N), mark(M))) [1] a__plus(N, 0) -> mark(N) [1] a__plus(N, s(M)) -> a__U11(tt, M, N) [1] mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3) [1] mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3) [1] mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) [1] mark(tt) -> tt [1] mark(s(X)) -> s(mark(X)) [1] mark(0) -> 0 [1] a__U11(X1, X2, X3) -> U11(X1, X2, X3) [1] a__U12(X1, X2, X3) -> U12(X1, X2, X3) [1] a__plus(X1, X2) -> plus(X1, X2) [1] The TRS has the following type information: a__U11 :: tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus tt :: tt:s:0:U11:U12:plus a__U12 :: tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus s :: tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus a__plus :: tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus mark :: tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus 0 :: tt:s:0:U11:U12:plus U11 :: tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus U12 :: tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus plus :: tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus -> tt:s:0:U11:U12: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__U11(tt, M, N) -> a__U12(tt, M, N) [1] a__U12(tt, M, N) -> s(a__plus(mark(N), mark(M))) [1] a__plus(N, 0) -> mark(N) [1] a__plus(N, s(M)) -> a__U11(tt, M, N) [1] mark(U11(U11(X120, X220, X313), X2, X3)) -> a__U11(a__U11(mark(X120), X220, X313), X2, X3) [2] mark(U11(U12(X121, X221, X314), X2, X3)) -> a__U11(a__U12(mark(X121), X221, X314), X2, X3) [2] mark(U11(plus(X122, X222), X2, X3)) -> a__U11(a__plus(mark(X122), mark(X222)), X2, X3) [2] mark(U11(tt, X2, X3)) -> a__U11(tt, X2, X3) [2] mark(U11(s(X9), X2, X3)) -> a__U11(s(mark(X9)), X2, X3) [2] mark(U11(0, X2, X3)) -> a__U11(0, X2, X3) [2] mark(U12(U11(X123, X223, X315), X2, X3)) -> a__U12(a__U11(mark(X123), X223, X315), X2, X3) [2] mark(U12(U12(X124, X224, X316), X2, X3)) -> a__U12(a__U12(mark(X124), X224, X316), X2, X3) [2] mark(U12(plus(X125, X225), X2, X3)) -> a__U12(a__plus(mark(X125), mark(X225)), X2, X3) [2] mark(U12(tt, X2, X3)) -> a__U12(tt, X2, X3) [2] mark(U12(s(X10), X2, X3)) -> a__U12(s(mark(X10)), X2, X3) [2] mark(U12(0, X2, X3)) -> a__U12(0, X2, X3) [2] mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) [1] mark(tt) -> tt [1] mark(s(X)) -> s(mark(X)) [1] mark(0) -> 0 [1] a__U11(X1, X2, X3) -> U11(X1, X2, X3) [1] a__U12(X1, X2, X3) -> U12(X1, X2, X3) [1] a__plus(X1, X2) -> plus(X1, X2) [1] The TRS has the following type information: a__U11 :: tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus tt :: tt:s:0:U11:U12:plus a__U12 :: tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus s :: tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus a__plus :: tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus mark :: tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus 0 :: tt:s:0:U11:U12:plus U11 :: tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus U12 :: tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus plus :: tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus -> tt:s:0:U11:U12: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__U11(z, z', z'') -{ 1 }-> a__U12(1, M, N) :|: z' = M, z = 1, z'' = N, M >= 0, N >= 0 a__U11(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__U12(z, z', z'') -{ 1 }-> 1 + a__plus(mark(N), mark(M)) :|: z' = M, z = 1, z'' = N, M >= 0, N >= 0 a__U12(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__plus(z, z') -{ 1 }-> mark(N) :|: z = N, z' = 0, N >= 0 a__plus(z, z') -{ 1 }-> a__U11(1, M, N) :|: 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__U12(a__plus(mark(X125), mark(X225)), X2, X3) :|: z = 1 + (1 + X125 + X225) + X2 + X3, X125 >= 0, X225 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U12(a__U12(mark(X124), X224, X316), X2, X3) :|: X124 >= 0, X224 >= 0, X3 >= 0, z = 1 + (1 + X124 + X224 + X316) + X2 + X3, X2 >= 0, X316 >= 0 mark(z) -{ 2 }-> a__U12(a__U11(mark(X123), X223, X315), X2, X3) :|: X223 >= 0, X315 >= 0, z = 1 + (1 + X123 + X223 + X315) + X2 + X3, X3 >= 0, X123 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U12(1, X2, X3) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U12(0, X2, X3) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U12(1 + mark(X10), X2, X3) :|: z = 1 + (1 + X10) + X2 + X3, X10 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__plus(mark(X122), mark(X222)), X2, X3) :|: z = 1 + (1 + X122 + X222) + X2 + X3, X222 >= 0, X3 >= 0, X122 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U12(mark(X121), X221, X314), X2, X3) :|: z = 1 + (1 + X121 + X221 + X314) + X2 + X3, X3 >= 0, X221 >= 0, X314 >= 0, X2 >= 0, X121 >= 0 mark(z) -{ 2 }-> a__U11(a__U11(mark(X120), X220, X313), X2, X3) :|: X120 >= 0, z = 1 + (1 + X120 + X220 + X313) + X2 + X3, X313 >= 0, X3 >= 0, X2 >= 0, X220 >= 0 mark(z) -{ 2 }-> a__U11(1, X2, X3) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(0, X2, X3) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(1 + mark(X9), X2, X3) :|: X9 >= 0, z = 1 + (1 + X9) + X2 + X3, X3 >= 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__U11(z, z', z'') -{ 1 }-> a__U12(1, z', z'') :|: z = 1, z' >= 0, z'' >= 0 a__U11(z, z', z'') -{ 1 }-> 1 + z + z' + z'' :|: z >= 0, z'' >= 0, z' >= 0 a__U12(z, z', z'') -{ 1 }-> 1 + a__plus(mark(z''), mark(z')) :|: z = 1, z' >= 0, z'' >= 0 a__U12(z, z', z'') -{ 1 }-> 1 + z + z' + z'' :|: z >= 0, z'' >= 0, z' >= 0 a__plus(z, z') -{ 1 }-> mark(z) :|: z' = 0, z >= 0 a__plus(z, z') -{ 1 }-> a__U11(1, z' - 1, z) :|: 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__U12(a__plus(mark(X125), mark(X225)), X2, X3) :|: z = 1 + (1 + X125 + X225) + X2 + X3, X125 >= 0, X225 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U12(a__U12(mark(X124), X224, X316), X2, X3) :|: X124 >= 0, X224 >= 0, X3 >= 0, z = 1 + (1 + X124 + X224 + X316) + X2 + X3, X2 >= 0, X316 >= 0 mark(z) -{ 2 }-> a__U12(a__U11(mark(X123), X223, X315), X2, X3) :|: X223 >= 0, X315 >= 0, z = 1 + (1 + X123 + X223 + X315) + X2 + X3, X3 >= 0, X123 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U12(1, X2, X3) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U12(0, X2, X3) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U12(1 + mark(X10), X2, X3) :|: z = 1 + (1 + X10) + X2 + X3, X10 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__plus(mark(X122), mark(X222)), X2, X3) :|: z = 1 + (1 + X122 + X222) + X2 + X3, X222 >= 0, X3 >= 0, X122 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U12(mark(X121), X221, X314), X2, X3) :|: z = 1 + (1 + X121 + X221 + X314) + X2 + X3, X3 >= 0, X221 >= 0, X314 >= 0, X2 >= 0, X121 >= 0 mark(z) -{ 2 }-> a__U11(a__U11(mark(X120), X220, X313), X2, X3) :|: X120 >= 0, z = 1 + (1 + X120 + X220 + X313) + X2 + X3, X313 >= 0, X3 >= 0, X2 >= 0, X220 >= 0 mark(z) -{ 2 }-> a__U11(1, X2, X3) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(0, X2, X3) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(1 + mark(X9), X2, X3) :|: X9 >= 0, z = 1 + (1 + X9) + X2 + X3, X3 >= 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__U11(tt, M, N) -> a__U12(tt, M, N) [1] a__U12(tt, M, N) -> s(a__plus(mark(N), mark(M))) [1] a__plus(N, 0) -> mark(N) [1] a__plus(N, s(M)) -> a__U11(tt, M, N) [1] mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3) [1] mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3) [1] mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) [1] mark(tt) -> tt [1] mark(s(X)) -> s(mark(X)) [1] mark(0) -> 0 [1] a__U11(X1, X2, X3) -> U11(X1, X2, X3) [1] a__U12(X1, X2, X3) -> U12(X1, X2, X3) [1] a__plus(X1, X2) -> plus(X1, X2) [1] The TRS has the following type information: a__U11 :: tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus tt :: tt:s:0:U11:U12:plus a__U12 :: tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus s :: tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus a__plus :: tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus mark :: tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus 0 :: tt:s:0:U11:U12:plus U11 :: tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus U12 :: tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus plus :: tt:s:0:U11:U12:plus -> tt:s:0:U11:U12:plus -> tt:s:0:U11:U12: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__U11(z, z', z'') -{ 1 }-> a__U12(1, M, N) :|: z' = M, z = 1, z'' = N, M >= 0, N >= 0 a__U11(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__U12(z, z', z'') -{ 1 }-> 1 + a__plus(mark(N), mark(M)) :|: z' = M, z = 1, z'' = N, M >= 0, N >= 0 a__U12(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__plus(z, z') -{ 1 }-> mark(N) :|: z = N, z' = 0, N >= 0 a__plus(z, z') -{ 1 }-> a__U11(1, M, N) :|: 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__U12(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> a__U11(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, 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 Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (21) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT ---------------------------------------- (22) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__U11(z0, z1, z2) -> c1 A__U12(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U12(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U12(z0, z1, z2) -> c4 A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) A__PLUS(z0, z1) -> c7 MARK(U11(z0, z1, z2)) -> c8(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c9(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c10(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c11(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(tt) -> c12 MARK(s(z0)) -> c13(MARK(z0)) MARK(0) -> c14 S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__U11(z0, z1, z2) -> c1 A__U12(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U12(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U12(z0, z1, z2) -> c4 A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) A__PLUS(z0, z1) -> c7 MARK(U11(z0, z1, z2)) -> c8(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c9(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c10(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c11(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(tt) -> c12 MARK(s(z0)) -> c13(MARK(z0)) MARK(0) -> c14 K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__U12_3, A__PLUS_2, MARK_1 Compound Symbols: c_1, c1, c2_2, c3_2, c4, c5_1, c6_1, c7, c8_2, c9_2, c10_2, c11_2, c12, c13_1, c14 ---------------------------------------- (23) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing nodes: A__U11(z0, z1, z2) -> c1 MARK(0) -> c14 A__PLUS(z0, z1) -> c7 A__U12(z0, z1, z2) -> c4 MARK(tt) -> c12 ---------------------------------------- (24) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__U12(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U12(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(U11(z0, z1, z2)) -> c8(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c9(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c10(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c11(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c13(MARK(z0)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__U12(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U12(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(U11(z0, z1, z2)) -> c8(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c9(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c10(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c11(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c13(MARK(z0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__U12_3, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_2, c3_2, c5_1, c6_1, c8_2, c9_2, c10_2, c11_2, c13_1 ---------------------------------------- (25) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U12(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1)) by A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U12(tt, tt, x1) -> c2(A__PLUS(mark(x1), tt), MARK(x1)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)), MARK(tt)) A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)), MARK(0)) ---------------------------------------- (26) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__U12(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(U11(z0, z1, z2)) -> c8(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c9(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c10(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c11(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U12(tt, tt, x1) -> c2(A__PLUS(mark(x1), tt), MARK(x1)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)), MARK(tt)) A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)), MARK(0)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__U12(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(U11(z0, z1, z2)) -> c8(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c9(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c10(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c11(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U12(tt, tt, x1) -> c2(A__PLUS(mark(x1), tt), MARK(x1)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)), MARK(tt)) A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__U12_3, A__PLUS_2, MARK_1 Compound Symbols: c_1, c3_2, c5_1, c6_1, c8_2, c9_2, c10_2, c11_2, c13_1, c2_2 ---------------------------------------- (27) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (28) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__U12(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(U11(z0, z1, z2)) -> c8(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c9(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c10(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c11(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__U12(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(U11(z0, z1, z2)) -> c8(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c9(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c10(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c11(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__U12_3, A__PLUS_2, MARK_1 Compound Symbols: c_1, c3_2, c5_1, c6_1, c8_2, c9_2, c10_2, c11_2, c13_1, c2_2, c2_1 ---------------------------------------- (29) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U12(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0)) by A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, tt, x1) -> c3(A__PLUS(mark(x1), tt), MARK(tt)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0), MARK(0)) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) ---------------------------------------- (30) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(U11(z0, z1, z2)) -> c8(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c9(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c10(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c11(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, tt, x1) -> c3(A__PLUS(mark(x1), tt), MARK(tt)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0), MARK(0)) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(U11(z0, z1, z2)) -> c8(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c9(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c10(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c11(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, tt, x1) -> c3(A__PLUS(mark(x1), tt), MARK(tt)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0), MARK(0)) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c8_2, c9_2, c10_2, c11_2, c13_1, c2_2, c2_1, c3_2 ---------------------------------------- (31) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__U12(tt, tt, x1) -> c3(A__PLUS(mark(x1), tt), MARK(tt)) ---------------------------------------- (32) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(U11(z0, z1, z2)) -> c8(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c9(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c10(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c11(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0), MARK(0)) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(U11(z0, z1, z2)) -> c8(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c9(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c10(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c11(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0), MARK(0)) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c8_2, c9_2, c10_2, c11_2, c13_1, c2_2, c2_1, c3_2 ---------------------------------------- (33) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (34) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(U11(z0, z1, z2)) -> c8(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c9(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c10(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c11(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(U11(z0, z1, z2)) -> c8(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c9(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c10(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c11(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c8_2, c9_2, c10_2, c11_2, c13_1, c2_2, c2_1, c3_2, c3_1 ---------------------------------------- (35) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U11(z0, z1, z2)) -> c8(A__U11(mark(z0), z1, z2), MARK(z0)) by MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2), MARK(tt)) MARK(U11(s(z0), x1, x2)) -> c8(A__U11(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U11(0, x1, x2)) -> c8(A__U11(0, x1, x2), MARK(0)) ---------------------------------------- (36) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(U12(z0, z1, z2)) -> c9(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c10(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c11(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2), MARK(tt)) MARK(U11(s(z0), x1, x2)) -> c8(A__U11(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U11(0, x1, x2)) -> c8(A__U11(0, x1, x2), MARK(0)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(U12(z0, z1, z2)) -> c9(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c10(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c11(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2), MARK(tt)) MARK(U11(s(z0), x1, x2)) -> c8(A__U11(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U11(0, x1, x2)) -> c8(A__U11(0, x1, x2), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c9_2, c10_2, c11_2, c13_1, c2_2, c2_1, c3_2, c3_1, c8_2 ---------------------------------------- (37) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(U11(0, x1, x2)) -> c8(A__U11(0, x1, x2), MARK(0)) ---------------------------------------- (38) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(U12(z0, z1, z2)) -> c9(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c10(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c11(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2), MARK(tt)) MARK(U11(s(z0), x1, x2)) -> c8(A__U11(s(mark(z0)), x1, x2), MARK(s(z0))) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(U12(z0, z1, z2)) -> c9(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c10(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c11(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2), MARK(tt)) MARK(U11(s(z0), x1, x2)) -> c8(A__U11(s(mark(z0)), x1, x2), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c9_2, c10_2, c11_2, c13_1, c2_2, c2_1, c3_2, c3_1, c8_2 ---------------------------------------- (39) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (40) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(U12(z0, z1, z2)) -> c9(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c10(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c11(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(U12(z0, z1, z2)) -> c9(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c10(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c11(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c9_2, c10_2, c11_2, c13_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1 ---------------------------------------- (41) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U12(z0, z1, z2)) -> c9(A__U12(mark(z0), z1, z2), MARK(z0)) by MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2), MARK(tt)) MARK(U12(s(z0), x1, x2)) -> c9(A__U12(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U12(0, x1, x2)) -> c9(A__U12(0, x1, x2), MARK(0)) ---------------------------------------- (42) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(plus(z0, z1)) -> c10(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c11(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2), MARK(tt)) MARK(U12(s(z0), x1, x2)) -> c9(A__U12(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U12(0, x1, x2)) -> c9(A__U12(0, x1, x2), MARK(0)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(plus(z0, z1)) -> c10(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c11(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2), MARK(tt)) MARK(U12(s(z0), x1, x2)) -> c9(A__U12(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U12(0, x1, x2)) -> c9(A__U12(0, x1, x2), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c10_2, c11_2, c13_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c9_2 ---------------------------------------- (43) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(U12(0, x1, x2)) -> c9(A__U12(0, x1, x2), MARK(0)) ---------------------------------------- (44) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(plus(z0, z1)) -> c10(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c11(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2), MARK(tt)) MARK(U12(s(z0), x1, x2)) -> c9(A__U12(s(mark(z0)), x1, x2), MARK(s(z0))) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(plus(z0, z1)) -> c10(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c11(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2), MARK(tt)) MARK(U12(s(z0), x1, x2)) -> c9(A__U12(s(mark(z0)), x1, x2), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c10_2, c11_2, c13_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c9_2 ---------------------------------------- (45) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (46) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(plus(z0, z1)) -> c10(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c11(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(plus(z0, z1)) -> c10(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c11(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c10_2, c11_2, c13_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c9_2, c9_1 ---------------------------------------- (47) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(z0, z1)) -> c10(A__PLUS(mark(z0), mark(z1)), MARK(z0)) by MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, tt)) -> c10(A__PLUS(mark(x0), tt), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1)), MARK(tt)) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1)), MARK(0)) ---------------------------------------- (48) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(plus(z0, z1)) -> c11(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, tt)) -> c10(A__PLUS(mark(x0), tt), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1)), MARK(tt)) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1)), MARK(0)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(plus(z0, z1)) -> c11(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, tt)) -> c10(A__PLUS(mark(x0), tt), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1)), MARK(tt)) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1)), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c11_2, c13_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c9_2, c9_1, c10_2 ---------------------------------------- (49) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (50) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(plus(z0, z1)) -> c11(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(plus(z0, z1)) -> c11(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c11_2, c13_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c9_2, c9_1, c10_2, c10_1 ---------------------------------------- (51) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(z0, z1)) -> c11(A__PLUS(mark(z0), mark(z1)), MARK(z1)) by MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, tt)) -> c11(A__PLUS(mark(x0), tt), MARK(tt)) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0), MARK(0)) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) ---------------------------------------- (52) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, tt)) -> c11(A__PLUS(mark(x0), tt), MARK(tt)) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0), MARK(0)) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, tt)) -> c11(A__PLUS(mark(x0), tt), MARK(tt)) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0), MARK(0)) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c9_2, c9_1, c10_2, c10_1, c11_2 ---------------------------------------- (53) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(plus(x0, tt)) -> c11(A__PLUS(mark(x0), tt), MARK(tt)) ---------------------------------------- (54) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0), MARK(0)) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0), MARK(0)) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c9_2, c9_1, c10_2, c10_1, c11_2 ---------------------------------------- (55) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (56) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c9_2, c9_1, c10_2, c10_1, c11_2, c11_1 ---------------------------------------- (57) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) by A__U12(tt, U11(x0, z1, z2), x3) -> c2(A__PLUS(mark(x3), U11(mark(x0), z1, z2)), MARK(x3)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(tt)) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(0)) ---------------------------------------- (58) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(x0, z1, z2), x3) -> c2(A__PLUS(mark(x3), U11(mark(x0), z1, z2)), MARK(x3)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(tt)) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(0)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(x0, z1, z2), x3) -> c2(A__PLUS(mark(x3), U11(mark(x0), z1, z2)), MARK(x3)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(tt)) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c9_2, c9_1, c10_2, c10_1, c11_2, c11_1 ---------------------------------------- (59) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (60) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c9_2, c9_1, c10_2, c10_1, c11_2, c11_1 ---------------------------------------- (61) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) by A__U12(tt, U12(x0, z1, z2), x3) -> c2(A__PLUS(mark(x3), U12(mark(x0), z1, z2)), MARK(x3)) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(tt)) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(0)) ---------------------------------------- (62) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(A__PLUS(mark(x3), U12(mark(x0), z1, z2)), MARK(x3)) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(tt)) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(0)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(A__PLUS(mark(x3), U12(mark(x0), z1, z2)), MARK(x3)) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(tt)) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c9_2, c9_1, c10_2, c10_1, c11_2, c11_1 ---------------------------------------- (63) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (64) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c9_2, c9_1, c10_2, c10_1, c11_2, c11_1 ---------------------------------------- (65) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) by A__U12(tt, plus(x0, x1), x2) -> c2(A__PLUS(mark(x2), plus(mark(x0), mark(x1))), MARK(x2)) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(tt)) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(0)) ---------------------------------------- (66) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, x1), x2) -> c2(A__PLUS(mark(x2), plus(mark(x0), mark(x1))), MARK(x2)) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(tt)) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(0)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, x1), x2) -> c2(A__PLUS(mark(x2), plus(mark(x0), mark(x1))), MARK(x2)) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(tt)) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c9_2, c9_1, c10_2, c10_1, c11_2, c11_1 ---------------------------------------- (67) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (68) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c9_2, c9_1, c10_2, c10_1, c11_2, c11_1 ---------------------------------------- (69) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) by A__U12(tt, U11(z0, z1, z2), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), a__U11(mark(z0), z1, z2)), MARK(U11(x1, x2, x3))) A__U12(tt, U12(z0, z1, z2), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), a__U12(mark(z0), z1, z2)), MARK(U11(x1, x2, x3))) A__U12(tt, plus(z0, z1), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), a__plus(mark(z0), mark(z1))), MARK(U11(x1, x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), tt), MARK(U11(x1, x2, x3))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(U11(0, x2, x3))) ---------------------------------------- (70) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), tt), MARK(U11(x1, x2, x3))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(U11(0, x2, x3))) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), tt), MARK(U11(x1, x2, x3))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(U11(0, x2, x3))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c9_2, c9_1, c10_2, c10_1, c11_2, c11_1 ---------------------------------------- (71) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (72) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c9_2, c9_1, c10_2, c10_1, c11_2, c11_1 ---------------------------------------- (73) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) by A__U12(tt, U11(z0, z1, z2), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), a__U11(mark(z0), z1, z2)), MARK(U12(x1, x2, x3))) A__U12(tt, U12(z0, z1, z2), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), a__U12(mark(z0), z1, z2)), MARK(U12(x1, x2, x3))) A__U12(tt, plus(z0, z1), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), a__plus(mark(z0), mark(z1))), MARK(U12(x1, x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), tt), MARK(U12(x1, x2, x3))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(U12(0, x2, x3))) ---------------------------------------- (74) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), tt), MARK(U12(x1, x2, x3))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(U12(0, x2, x3))) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), tt), MARK(U12(x1, x2, x3))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(U12(0, x2, x3))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c9_2, c9_1, c10_2, c10_1, c11_2, c11_1 ---------------------------------------- (75) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (76) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c9_2, c9_1, c10_2, c10_1, c11_2, c11_1 ---------------------------------------- (77) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) by A__U12(tt, U11(z0, z1, z2), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), a__U11(mark(z0), z1, z2)), MARK(plus(x1, x2))) A__U12(tt, U12(z0, z1, z2), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), a__U12(mark(z0), z1, z2)), MARK(plus(x1, x2))) A__U12(tt, plus(z0, z1), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), a__plus(mark(z0), mark(z1))), MARK(plus(x1, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), tt), MARK(plus(x1, x2))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) ---------------------------------------- (78) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, tt, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), tt), MARK(plus(x1, x2))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, tt, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), tt), MARK(plus(x1, x2))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c9_2, c9_1, c10_2, c10_1, c11_2, c11_1 ---------------------------------------- (79) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (80) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c9_2, c9_1, c10_2, c10_1, c11_2, c11_1 ---------------------------------------- (81) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) by A__U12(tt, U11(z0, z1, z2), s(x1)) -> c2(A__PLUS(s(mark(x1)), a__U11(mark(z0), z1, z2)), MARK(s(x1))) A__U12(tt, U12(z0, z1, z2), s(x1)) -> c2(A__PLUS(s(mark(x1)), a__U12(mark(z0), z1, z2)), MARK(s(x1))) A__U12(tt, plus(z0, z1), s(x1)) -> c2(A__PLUS(s(mark(x1)), a__plus(mark(z0), mark(z1))), MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(A__PLUS(s(mark(x1)), tt), MARK(s(x1))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) ---------------------------------------- (82) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, tt, s(x1)) -> c2(A__PLUS(s(mark(x1)), tt), MARK(s(x1))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, tt, s(x1)) -> c2(A__PLUS(s(mark(x1)), tt), MARK(s(x1))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c9_2, c9_1, c10_2, c10_1, c11_2, c11_1 ---------------------------------------- (83) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (84) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c9_2, c9_1, c10_2, c10_1, c11_2, c11_1 ---------------------------------------- (85) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) by A__U12(tt, U11(z0, z1, z2), tt) -> c2(A__PLUS(tt, a__U11(mark(z0), z1, z2))) A__U12(tt, U12(z0, z1, z2), tt) -> c2(A__PLUS(tt, a__U12(mark(z0), z1, z2))) A__U12(tt, plus(z0, z1), tt) -> c2(A__PLUS(tt, a__plus(mark(z0), mark(z1)))) A__U12(tt, tt, tt) -> c2(A__PLUS(tt, tt)) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) ---------------------------------------- (86) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, tt) -> c2(A__PLUS(tt, tt)) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, 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A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), 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c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, tt) -> c2(A__PLUS(tt, tt)) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c9_2, c9_1, c10_2, c10_1, c11_2, c11_1 ---------------------------------------- (87) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__U12(tt, tt, tt) -> c2(A__PLUS(tt, tt)) ---------------------------------------- (88) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c9_2, c9_1, c10_2, c10_1, c11_2, c11_1 ---------------------------------------- (89) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) by A__U12(tt, U11(z0, z1, z2), 0) -> c2(A__PLUS(0, a__U11(mark(z0), z1, z2))) A__U12(tt, U12(z0, z1, z2), 0) -> c2(A__PLUS(0, a__U12(mark(z0), z1, z2))) A__U12(tt, plus(z0, z1), 0) -> c2(A__PLUS(0, a__plus(mark(z0), mark(z1)))) A__U12(tt, tt, 0) -> c2(A__PLUS(0, tt)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) ---------------------------------------- (90) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, tt, 0) -> c2(A__PLUS(0, tt)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, tt, 0) -> c2(A__PLUS(0, tt)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c9_2, c9_1, c10_2, c10_1, c11_2, c11_1 ---------------------------------------- (91) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__U12(tt, tt, 0) -> c2(A__PLUS(0, tt)) ---------------------------------------- (92) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c9_2, c9_1, c10_2, c10_1, c11_2, c11_1 ---------------------------------------- (93) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) by A__U12(tt, U11(x0, z1, z2), x3) -> c3(A__PLUS(mark(x3), U11(mark(x0), z1, z2)), MARK(U11(x0, z1, z2))) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(U11(0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) ---------------------------------------- (94) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(x0, z1, z2), x3) -> c3(A__PLUS(mark(x3), U11(mark(x0), z1, z2)), MARK(U11(x0, z1, z2))) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(U11(0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(x0, z1, z2), x3) -> c3(A__PLUS(mark(x3), U11(mark(x0), z1, z2)), MARK(U11(x0, z1, z2))) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(U11(0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c9_2, c9_1, c10_2, c10_1, c11_2, c11_1 ---------------------------------------- (95) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (96) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c9_2, c9_1, c10_2, c10_1, c11_2, c11_1 ---------------------------------------- (97) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) by A__U12(tt, U12(x0, z1, z2), x3) -> c3(A__PLUS(mark(x3), U12(mark(x0), z1, z2)), MARK(U12(x0, z1, z2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(U12(0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) ---------------------------------------- (98) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), 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c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(A__PLUS(mark(x3), U12(mark(x0), z1, z2)), MARK(U12(x0, z1, z2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(U12(0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(A__PLUS(mark(x3), U12(mark(x0), z1, z2)), MARK(U12(x0, z1, z2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(U12(0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c9_2, c9_1, c10_2, c10_1, c11_2, c11_1 ---------------------------------------- (99) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (100) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c9_2, c9_1, c10_2, c10_1, c11_2, c11_1 ---------------------------------------- (101) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) by A__U12(tt, plus(x0, x1), x2) -> c3(A__PLUS(mark(x2), plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) ---------------------------------------- (102) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, x1), x2) -> c3(A__PLUS(mark(x2), plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) 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z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, x1), x2) -> c3(A__PLUS(mark(x2), plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c9_2, c9_1, c10_2, c10_1, c11_2, c11_1 ---------------------------------------- (103) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (104) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> 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a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c9_2, c9_1, c10_2, c10_1, c11_2, c11_1 ---------------------------------------- (105) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) by A__U12(tt, U11(z0, z1, z2), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, tt, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), tt), MARK(tt)) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(0)) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) ---------------------------------------- (106) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, tt, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), tt), MARK(tt)) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(0)) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), 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c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, tt, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), tt), MARK(tt)) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(0)) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c9_2, c9_1, c10_2, c10_1, c11_2, c11_1 ---------------------------------------- (107) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__U12(tt, tt, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), tt), MARK(tt)) ---------------------------------------- (108) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, 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x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(0)) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), 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x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), 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A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, 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x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(0)) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c9_2, c9_1, c10_2, c10_1, c11_2, c11_1 ---------------------------------------- (109) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (110) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c9_2, c9_1, c10_2, c10_1, c11_2, c11_1 ---------------------------------------- (111) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) by A__U12(tt, U11(z0, z1, z2), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, tt, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), tt), MARK(tt)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(0)) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) ---------------------------------------- (112) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, tt, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), tt), MARK(tt)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(0)) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) 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z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, tt, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), tt), MARK(tt)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(0)) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c9_2, c9_1, c10_2, c10_1, c11_2, c11_1 ---------------------------------------- (113) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__U12(tt, tt, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), tt), MARK(tt)) ---------------------------------------- (114) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> 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0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(0)) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), 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x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(0)) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c9_2, c9_1, c10_2, c10_1, c11_2, c11_1 ---------------------------------------- (115) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (116) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c9_2, c9_1, c10_2, c10_1, c11_2, c11_1 ---------------------------------------- (117) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) by A__U12(tt, U11(z0, z1, z2), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, tt, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), tt), MARK(tt)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(0)) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) ---------------------------------------- (118) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), 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MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, tt, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), tt), MARK(tt)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(0)) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, 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c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, tt, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), tt), MARK(tt)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(0)) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c9_2, c9_1, c10_2, c10_1, c11_2, c11_1 ---------------------------------------- (119) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__U12(tt, tt, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), tt), MARK(tt)) ---------------------------------------- (120) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(0)) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, 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A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> 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A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), 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x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, 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MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(0)) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c9_2, c9_1, c10_2, c10_1, c11_2, c11_1 ---------------------------------------- (121) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (122) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) 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x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), 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z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, 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a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c9_2, c9_1, c10_2, c10_1, c11_2, c11_1 ---------------------------------------- (123) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) by A__U12(tt, U11(z0, z1, z2), tt) -> c3(A__PLUS(tt, a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), tt) -> c3(A__PLUS(tt, a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), tt) -> c3(A__PLUS(tt, a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, tt, tt) -> c3(A__PLUS(tt, tt), MARK(tt)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, tt) -> c3(A__PLUS(tt, 0), MARK(0)) ---------------------------------------- (124) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), 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A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, tt, tt) -> c3(A__PLUS(tt, tt), MARK(tt)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, tt) -> c3(A__PLUS(tt, 0), MARK(0)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, 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A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> 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A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), 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x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, 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MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, tt, tt) -> c3(A__PLUS(tt, tt), MARK(tt)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, tt) -> c3(A__PLUS(tt, 0), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c9_2, c9_1, c10_2, c10_1, c11_2, c11_1 ---------------------------------------- (125) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__U12(tt, tt, tt) -> c3(A__PLUS(tt, tt), MARK(tt)) ---------------------------------------- (126) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, 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c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, tt) -> c3(A__PLUS(tt, 0), MARK(0)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), 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a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> 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a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, tt) -> c3(A__PLUS(tt, 0), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c9_2, c9_1, c10_2, c10_1, c11_2, c11_1 ---------------------------------------- (127) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (128) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, tt) -> c3(A__PLUS(tt, 0)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), 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MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, tt) -> c3(A__PLUS(tt, 0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c9_2, c9_1, c10_2, c10_1, c11_2, c11_1 ---------------------------------------- (129) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) by A__U12(tt, U11(z0, z1, z2), s(x1)) -> c3(A__PLUS(s(mark(x1)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), s(x1)) -> c3(A__PLUS(s(mark(x1)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), s(x1)) -> c3(A__PLUS(s(mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, tt, s(x1)) -> c3(A__PLUS(s(mark(x1)), tt), MARK(tt)) A__U12(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0), MARK(0)) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c3(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c3(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U12(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) ---------------------------------------- (130) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U12(tt, tt, s(x1)) -> c3(A__PLUS(s(mark(x1)), tt), MARK(tt)) A__U12(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0), MARK(0)) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c3(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c3(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U12(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, 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c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U12(tt, tt, s(x1)) -> c3(A__PLUS(s(mark(x1)), tt), MARK(tt)) A__U12(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0), MARK(0)) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c3(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c3(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U12(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c9_2, c9_1, c10_2, c10_1, c11_2, c11_1 ---------------------------------------- (131) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__U12(tt, tt, s(x1)) -> c3(A__PLUS(s(mark(x1)), tt), MARK(tt)) ---------------------------------------- (132) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U12(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0), MARK(0)) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c3(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c3(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U12(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U12(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0), MARK(0)) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c3(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c3(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U12(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c9_2, c9_1, c10_2, c10_1, c11_2, c11_1 ---------------------------------------- (133) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (134) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> 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U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, 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A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U12(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c3(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c3(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U12(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U12(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U12(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c3(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c3(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U12(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U12(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c9_2, c9_1, c10_2, c10_1, c11_2, c11_1 ---------------------------------------- (135) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) by A__U12(tt, U11(z0, z1, z2), 0) -> c3(A__PLUS(0, a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(z0, z1, z2), 0) -> c3(A__PLUS(0, a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U12(tt, plus(z0, z1), 0) -> c3(A__PLUS(0, a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U12(tt, tt, 0) -> c3(A__PLUS(0, tt), MARK(tt)) A__U12(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, 0) -> c3(A__PLUS(0, 0), MARK(0)) ---------------------------------------- (136) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U12(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c3(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c3(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U12(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U12(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U12(tt, tt, 0) -> c3(A__PLUS(0, tt), MARK(tt)) A__U12(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, 0) -> c3(A__PLUS(0, 0), MARK(0)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U12(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c3(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c3(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U12(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U12(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U12(tt, tt, 0) -> c3(A__PLUS(0, tt), MARK(tt)) A__U12(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, 0) -> c3(A__PLUS(0, 0), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c9_2, c9_1, c10_2, c10_1, c11_2, c11_1 ---------------------------------------- (137) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__U12(tt, tt, 0) -> c3(A__PLUS(0, tt), MARK(tt)) ---------------------------------------- (138) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U12(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c3(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c3(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U12(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U12(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U12(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, 0) -> c3(A__PLUS(0, 0), MARK(0)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), 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x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U12(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c3(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c3(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U12(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U12(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U12(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, 0) -> c3(A__PLUS(0, 0), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c9_2, c9_1, c10_2, c10_1, c11_2, c11_1 ---------------------------------------- (139) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (140) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), 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A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U12(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c3(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c3(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U12(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U12(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U12(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, 0) -> c3(A__PLUS(0, 0)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), 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c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U12(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c3(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c3(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U12(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U12(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U12(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, 0) -> c3(A__PLUS(0, 0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c9_2, c9_1, c10_2, c10_1, c11_2, c11_1 ---------------------------------------- (141) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U11(U11(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) by MARK(U11(U11(x0, z1, z2), x3, x4)) -> c8(A__U11(U11(mark(x0), z1, z2), x3, x4), MARK(U11(x0, z1, z2))) MARK(U11(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U11(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U11(U11(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U11(U11(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U11(U11(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U11(U11(0, x1, x2), x3, x4)) -> c8(A__U11(a__U11(0, x1, x2), x3, x4), MARK(U11(0, x1, x2))) ---------------------------------------- (142) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U12(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c3(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c3(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U12(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U12(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U12(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, 0) -> c3(A__PLUS(0, 0)) MARK(U11(U11(x0, z1, z2), x3, x4)) -> c8(A__U11(U11(mark(x0), z1, z2), x3, x4), MARK(U11(x0, z1, z2))) MARK(U11(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U11(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U11(U11(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U11(U11(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U11(U11(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U11(U11(0, x1, x2), x3, x4)) -> c8(A__U11(a__U11(0, x1, x2), x3, x4), MARK(U11(0, x1, x2))) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U12(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c3(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c3(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U12(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U12(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U12(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, 0) -> c3(A__PLUS(0, 0)) MARK(U11(U11(x0, z1, z2), x3, x4)) -> c8(A__U11(U11(mark(x0), z1, z2), x3, x4), MARK(U11(x0, z1, z2))) MARK(U11(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U11(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U11(U11(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U11(U11(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U11(U11(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U11(U11(0, x1, x2), x3, x4)) -> c8(A__U11(a__U11(0, x1, x2), x3, x4), MARK(U11(0, x1, x2))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c9_2, c9_1, c10_2, c10_1, c11_2, c11_1 ---------------------------------------- (143) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (144) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U12(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c3(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c3(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U12(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U12(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U12(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, 0) -> c3(A__PLUS(0, 0)) MARK(U11(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U11(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U11(U11(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U11(U11(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U11(U11(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U11(U11(x0, z1, z2), x3, x4)) -> c8(MARK(U11(x0, z1, z2))) MARK(U11(U11(0, x1, x2), x3, x4)) -> c8(A__U11(a__U11(0, x1, x2), x3, x4)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U12(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c3(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c3(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U12(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U12(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U12(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, 0) -> c3(A__PLUS(0, 0)) MARK(U11(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U11(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U11(U11(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U11(U11(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U11(U11(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U11(U11(x0, z1, z2), x3, x4)) -> c8(MARK(U11(x0, z1, z2))) MARK(U11(U11(0, x1, x2), x3, x4)) -> c8(A__U11(a__U11(0, x1, x2), x3, x4)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c9_2, c9_1, c10_2, c10_1, c11_2, c11_1 ---------------------------------------- (145) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U11(U12(z0, z1, z2), x1, x2)) -> c8(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) by MARK(U11(U12(x0, z1, z2), x3, x4)) -> c8(A__U11(U12(mark(x0), z1, z2), x3, x4), MARK(U12(x0, z1, z2))) MARK(U11(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U11(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U11(U12(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U11(U12(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U11(U12(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U11(U12(0, x1, x2), x3, x4)) -> c8(A__U11(a__U12(0, x1, x2), x3, x4), MARK(U12(0, x1, x2))) ---------------------------------------- (146) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U12(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c3(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c3(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U12(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U12(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U12(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, 0) -> c3(A__PLUS(0, 0)) MARK(U11(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U11(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U11(U11(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U11(U11(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U11(U11(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U11(U11(x0, z1, z2), x3, x4)) -> c8(MARK(U11(x0, z1, z2))) MARK(U11(U11(0, x1, x2), x3, x4)) -> c8(A__U11(a__U11(0, x1, x2), x3, x4)) MARK(U11(U12(x0, z1, z2), x3, x4)) -> c8(A__U11(U12(mark(x0), z1, z2), x3, x4), MARK(U12(x0, z1, z2))) MARK(U11(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U11(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U11(U12(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U11(U12(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U11(U12(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U11(U12(0, x1, x2), x3, x4)) -> c8(A__U11(a__U12(0, x1, x2), x3, x4), MARK(U12(0, x1, x2))) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), 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MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U12(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c3(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c3(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U12(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U12(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U12(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, 0) -> c3(A__PLUS(0, 0)) MARK(U11(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U11(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U11(U11(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U11(U11(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U11(U11(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U11(U11(x0, z1, z2), x3, x4)) -> c8(MARK(U11(x0, z1, z2))) MARK(U11(U11(0, x1, x2), x3, x4)) -> c8(A__U11(a__U11(0, x1, x2), x3, x4)) MARK(U11(U12(x0, z1, z2), x3, x4)) -> c8(A__U11(U12(mark(x0), z1, z2), x3, x4), MARK(U12(x0, z1, z2))) MARK(U11(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U11(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U11(U12(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U11(U12(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U11(U12(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U11(U12(0, x1, x2), x3, x4)) -> c8(A__U11(a__U12(0, x1, x2), x3, x4), MARK(U12(0, x1, x2))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c9_2, c9_1, c10_2, c10_1, c11_2, c11_1 ---------------------------------------- (147) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (148) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U12(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c3(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c3(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U12(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U12(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U12(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, 0) -> c3(A__PLUS(0, 0)) MARK(U11(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U11(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U11(U11(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U11(U11(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U11(U11(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U11(U11(x0, z1, z2), x3, x4)) -> c8(MARK(U11(x0, z1, z2))) MARK(U11(U11(0, x1, x2), x3, x4)) -> c8(A__U11(a__U11(0, x1, x2), x3, x4)) MARK(U11(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U11(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U11(U12(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U11(U12(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U11(U12(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U11(U12(x0, z1, z2), x3, x4)) -> c8(MARK(U12(x0, z1, z2))) MARK(U11(U12(0, x1, x2), x3, x4)) -> c8(A__U11(a__U12(0, x1, x2), x3, x4)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), 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MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U12(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c3(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c3(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U12(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U12(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U12(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, 0) -> c3(A__PLUS(0, 0)) MARK(U11(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U11(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U11(U11(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U11(U11(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U11(U11(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U11(U11(x0, z1, z2), x3, x4)) -> c8(MARK(U11(x0, z1, z2))) MARK(U11(U11(0, x1, x2), x3, x4)) -> c8(A__U11(a__U11(0, x1, x2), x3, x4)) MARK(U11(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U11(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U11(U12(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U11(U12(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U11(U12(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U11(U12(x0, z1, z2), x3, x4)) -> c8(MARK(U12(x0, z1, z2))) MARK(U11(U12(0, x1, x2), x3, x4)) -> c8(A__U11(a__U12(0, x1, x2), x3, x4)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c9_2, c9_1, c10_2, c10_1, c11_2, c11_1 ---------------------------------------- (149) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U11(plus(z0, z1), x1, x2)) -> c8(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) by MARK(U11(plus(x0, x1), x2, x3)) -> c8(A__U11(plus(mark(x0), mark(x1)), x2, x3), MARK(plus(x0, x1))) MARK(U11(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U11(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U11(plus(x0, plus(z0, z1)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U11(plus(x0, tt), x2, x3)) -> c8(A__U11(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U11(plus(x0, s(z0)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U11(plus(x0, 0), x2, x3)) -> c8(A__U11(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U11(plus(U11(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U11(plus(U12(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U11(plus(plus(z0, z1), x1), x2, x3)) -> c8(A__U11(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U11(plus(tt, x1), x2, x3)) -> c8(A__U11(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U11(plus(s(z0), x1), x2, x3)) -> c8(A__U11(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U11(plus(0, x1), x2, x3)) -> c8(A__U11(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) ---------------------------------------- (150) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U12(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c3(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c3(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U12(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U12(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U12(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, 0) -> c3(A__PLUS(0, 0)) MARK(U11(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U11(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U11(U11(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U11(U11(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U11(U11(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U11(U11(x0, z1, z2), x3, x4)) -> c8(MARK(U11(x0, z1, z2))) MARK(U11(U11(0, x1, x2), x3, x4)) -> c8(A__U11(a__U11(0, x1, x2), x3, x4)) MARK(U11(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U11(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U11(U12(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U11(U12(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U11(U12(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U11(U12(x0, z1, z2), x3, x4)) -> c8(MARK(U12(x0, z1, z2))) MARK(U11(U12(0, x1, x2), x3, x4)) -> c8(A__U11(a__U12(0, x1, x2), x3, x4)) MARK(U11(plus(x0, x1), x2, x3)) -> c8(A__U11(plus(mark(x0), mark(x1)), x2, x3), MARK(plus(x0, x1))) MARK(U11(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U11(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U11(plus(x0, plus(z0, z1)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U11(plus(x0, tt), x2, x3)) -> c8(A__U11(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U11(plus(x0, s(z0)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U11(plus(x0, 0), x2, x3)) -> c8(A__U11(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U11(plus(U11(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U11(plus(U12(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U11(plus(plus(z0, z1), x1), x2, x3)) -> c8(A__U11(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U11(plus(tt, x1), x2, x3)) -> c8(A__U11(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U11(plus(s(z0), x1), x2, x3)) -> c8(A__U11(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U11(plus(0, x1), x2, x3)) -> c8(A__U11(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 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x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U12(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c3(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c3(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U12(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U12(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U12(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, 0) -> c3(A__PLUS(0, 0)) MARK(U11(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U11(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U11(U11(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U11(U11(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U11(U11(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U11(U11(x0, z1, z2), x3, x4)) -> c8(MARK(U11(x0, z1, z2))) MARK(U11(U11(0, x1, x2), x3, x4)) -> c8(A__U11(a__U11(0, x1, x2), x3, x4)) MARK(U11(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U11(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U11(U12(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U11(U12(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U11(U12(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U11(U12(x0, z1, z2), x3, x4)) -> c8(MARK(U12(x0, z1, z2))) MARK(U11(U12(0, x1, x2), x3, x4)) -> c8(A__U11(a__U12(0, x1, x2), x3, x4)) MARK(U11(plus(x0, x1), x2, x3)) -> c8(A__U11(plus(mark(x0), mark(x1)), x2, x3), MARK(plus(x0, x1))) MARK(U11(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U11(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U11(plus(x0, plus(z0, z1)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U11(plus(x0, tt), x2, x3)) -> c8(A__U11(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U11(plus(x0, s(z0)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U11(plus(x0, 0), x2, x3)) -> c8(A__U11(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U11(plus(U11(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U11(plus(U12(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U11(plus(plus(z0, z1), x1), x2, x3)) -> c8(A__U11(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U11(plus(tt, x1), x2, x3)) -> c8(A__U11(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U11(plus(s(z0), x1), x2, x3)) -> c8(A__U11(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U11(plus(0, x1), x2, x3)) -> c8(A__U11(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_1, c9_2, c9_1, c10_2, c10_1, c11_2, c11_1, c8_2 ---------------------------------------- (151) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (152) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U12(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c3(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c3(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U12(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U12(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U12(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, 0) -> c3(A__PLUS(0, 0)) MARK(U11(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U11(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U11(U11(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U11(U11(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U11(U11(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U11(U11(x0, z1, z2), x3, x4)) -> c8(MARK(U11(x0, z1, z2))) MARK(U11(U11(0, x1, x2), x3, x4)) -> c8(A__U11(a__U11(0, x1, x2), x3, x4)) MARK(U11(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U11(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U11(U12(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U11(U12(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U11(U12(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U11(U12(x0, z1, z2), x3, x4)) -> c8(MARK(U12(x0, z1, z2))) MARK(U11(U12(0, x1, x2), x3, x4)) -> c8(A__U11(a__U12(0, x1, x2), x3, x4)) MARK(U11(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U11(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U11(plus(x0, plus(z0, z1)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U11(plus(x0, tt), x2, x3)) -> c8(A__U11(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U11(plus(x0, s(z0)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U11(plus(x0, 0), x2, x3)) -> c8(A__U11(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U11(plus(U11(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U11(plus(U12(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U11(plus(plus(z0, z1), x1), x2, x3)) -> c8(A__U11(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U11(plus(tt, x1), x2, x3)) -> c8(A__U11(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U11(plus(s(z0), x1), x2, x3)) -> c8(A__U11(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U11(plus(0, x1), x2, x3)) -> c8(A__U11(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U11(plus(x0, x1), x2, x3)) -> c8(MARK(plus(x0, x1))) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U12(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c3(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c3(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U12(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U12(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U12(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, 0) -> c3(A__PLUS(0, 0)) MARK(U11(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U11(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U11(U11(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U11(U11(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U11(U11(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U11(U11(x0, z1, z2), x3, x4)) -> c8(MARK(U11(x0, z1, z2))) MARK(U11(U11(0, x1, x2), x3, x4)) -> c8(A__U11(a__U11(0, x1, x2), x3, x4)) MARK(U11(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U11(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U11(U12(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U11(U12(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U11(U12(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U11(U12(x0, z1, z2), x3, x4)) -> c8(MARK(U12(x0, z1, z2))) MARK(U11(U12(0, x1, x2), x3, x4)) -> c8(A__U11(a__U12(0, x1, x2), x3, x4)) MARK(U11(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U11(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U11(plus(x0, plus(z0, z1)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U11(plus(x0, tt), x2, x3)) -> c8(A__U11(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U11(plus(x0, s(z0)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U11(plus(x0, 0), x2, x3)) -> c8(A__U11(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U11(plus(U11(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U11(plus(U12(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U11(plus(plus(z0, z1), x1), x2, x3)) -> c8(A__U11(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U11(plus(tt, x1), x2, x3)) -> c8(A__U11(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U11(plus(s(z0), x1), x2, x3)) -> c8(A__U11(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U11(plus(0, x1), x2, x3)) -> c8(A__U11(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U11(plus(x0, x1), x2, x3)) -> c8(MARK(plus(x0, x1))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_1, c9_2, c9_1, c10_2, c10_1, c11_2, c11_1, c8_2 ---------------------------------------- (153) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U12(U11(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) by MARK(U12(U11(x0, z1, z2), x3, x4)) -> c9(A__U12(U11(mark(x0), z1, z2), x3, x4), MARK(U11(x0, z1, z2))) MARK(U12(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U12(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U12(U11(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U12(U11(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U12(U11(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U12(U11(0, x1, x2), x3, x4)) -> c9(A__U12(a__U11(0, x1, x2), x3, x4), MARK(U11(0, x1, x2))) ---------------------------------------- (154) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U12(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c3(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c3(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U12(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U12(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U12(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, 0) -> c3(A__PLUS(0, 0)) MARK(U11(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U11(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U11(U11(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U11(U11(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U11(U11(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U11(U11(x0, z1, z2), x3, x4)) -> c8(MARK(U11(x0, z1, z2))) MARK(U11(U11(0, x1, x2), x3, x4)) -> c8(A__U11(a__U11(0, x1, x2), x3, x4)) MARK(U11(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U11(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U11(U12(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U11(U12(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U11(U12(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U11(U12(x0, z1, z2), x3, x4)) -> c8(MARK(U12(x0, z1, z2))) MARK(U11(U12(0, x1, x2), x3, x4)) -> c8(A__U11(a__U12(0, x1, x2), x3, x4)) MARK(U11(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U11(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U11(plus(x0, plus(z0, z1)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U11(plus(x0, tt), x2, x3)) -> c8(A__U11(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U11(plus(x0, s(z0)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U11(plus(x0, 0), x2, x3)) -> c8(A__U11(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U11(plus(U11(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U11(plus(U12(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U11(plus(plus(z0, z1), x1), x2, x3)) -> c8(A__U11(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U11(plus(tt, x1), x2, x3)) -> c8(A__U11(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U11(plus(s(z0), x1), x2, x3)) -> c8(A__U11(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U11(plus(0, x1), x2, x3)) -> c8(A__U11(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U11(plus(x0, x1), x2, x3)) -> c8(MARK(plus(x0, x1))) MARK(U12(U11(x0, z1, z2), x3, x4)) -> c9(A__U12(U11(mark(x0), z1, z2), x3, x4), MARK(U11(x0, z1, z2))) MARK(U12(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U12(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U12(U11(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U12(U11(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U12(U11(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U12(U11(0, x1, x2), x3, x4)) -> c9(A__U12(a__U11(0, x1, x2), x3, x4), MARK(U11(0, x1, x2))) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), 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plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U12(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c3(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c3(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U12(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U12(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U12(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, 0) -> c3(A__PLUS(0, 0)) MARK(U11(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U11(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U11(U11(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U11(U11(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U11(U11(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U11(U11(x0, z1, z2), x3, x4)) -> c8(MARK(U11(x0, z1, z2))) MARK(U11(U11(0, x1, x2), x3, x4)) -> c8(A__U11(a__U11(0, x1, x2), x3, x4)) MARK(U11(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U11(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U11(U12(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U11(U12(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U11(U12(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U11(U12(x0, z1, z2), x3, x4)) -> c8(MARK(U12(x0, z1, z2))) MARK(U11(U12(0, x1, x2), x3, x4)) -> c8(A__U11(a__U12(0, x1, x2), x3, x4)) MARK(U11(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U11(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U11(plus(x0, plus(z0, z1)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U11(plus(x0, tt), x2, x3)) -> c8(A__U11(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U11(plus(x0, s(z0)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U11(plus(x0, 0), x2, x3)) -> c8(A__U11(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U11(plus(U11(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U11(plus(U12(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U11(plus(plus(z0, z1), x1), x2, x3)) -> c8(A__U11(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U11(plus(tt, x1), x2, x3)) -> c8(A__U11(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U11(plus(s(z0), x1), x2, x3)) -> c8(A__U11(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U11(plus(0, x1), x2, x3)) -> c8(A__U11(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U11(plus(x0, x1), x2, x3)) -> c8(MARK(plus(x0, x1))) MARK(U12(U11(x0, z1, z2), x3, x4)) -> c9(A__U12(U11(mark(x0), z1, z2), x3, x4), MARK(U11(x0, z1, z2))) MARK(U12(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U12(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U12(U11(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U12(U11(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U12(U11(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U12(U11(0, x1, x2), x3, x4)) -> c9(A__U12(a__U11(0, x1, x2), x3, x4), MARK(U11(0, x1, x2))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_1, c9_2, c9_1, c10_2, c10_1, c11_2, c11_1, c8_2 ---------------------------------------- (155) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (156) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, 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A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U12(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c3(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c3(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U12(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U12(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U12(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, 0) -> c3(A__PLUS(0, 0)) MARK(U11(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U11(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U11(U11(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U11(U11(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U11(U11(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U11(U11(x0, z1, z2), x3, x4)) -> c8(MARK(U11(x0, z1, z2))) MARK(U11(U11(0, x1, x2), x3, x4)) -> c8(A__U11(a__U11(0, x1, x2), x3, x4)) MARK(U11(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U11(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U11(U12(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U11(U12(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U11(U12(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U11(U12(x0, z1, z2), x3, x4)) -> c8(MARK(U12(x0, z1, z2))) MARK(U11(U12(0, x1, x2), x3, x4)) -> c8(A__U11(a__U12(0, x1, x2), x3, x4)) MARK(U11(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U11(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U11(plus(x0, plus(z0, z1)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U11(plus(x0, tt), x2, x3)) -> c8(A__U11(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U11(plus(x0, s(z0)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U11(plus(x0, 0), x2, x3)) -> c8(A__U11(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U11(plus(U11(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U11(plus(U12(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U11(plus(plus(z0, z1), x1), x2, x3)) -> c8(A__U11(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U11(plus(tt, x1), x2, x3)) -> c8(A__U11(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U11(plus(s(z0), x1), x2, x3)) -> c8(A__U11(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U11(plus(0, x1), x2, x3)) -> c8(A__U11(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U11(plus(x0, x1), x2, x3)) -> c8(MARK(plus(x0, x1))) MARK(U12(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U12(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U12(U11(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U12(U11(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U12(U11(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U12(U11(x0, z1, z2), x3, x4)) -> c9(MARK(U11(x0, z1, z2))) MARK(U12(U11(0, x1, x2), x3, x4)) -> c9(A__U12(a__U11(0, x1, x2), x3, x4)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U12(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c3(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c3(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U12(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U12(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U12(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, 0) -> c3(A__PLUS(0, 0)) MARK(U11(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U11(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U11(U11(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U11(U11(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U11(U11(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U11(U11(x0, z1, z2), x3, x4)) -> c8(MARK(U11(x0, z1, z2))) MARK(U11(U11(0, x1, x2), x3, x4)) -> c8(A__U11(a__U11(0, x1, x2), x3, x4)) MARK(U11(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U11(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U11(U12(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U11(U12(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U11(U12(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U11(U12(x0, z1, z2), x3, x4)) -> c8(MARK(U12(x0, z1, z2))) MARK(U11(U12(0, x1, x2), x3, x4)) -> c8(A__U11(a__U12(0, x1, x2), x3, x4)) MARK(U11(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U11(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U11(plus(x0, plus(z0, z1)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U11(plus(x0, tt), x2, x3)) -> c8(A__U11(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U11(plus(x0, s(z0)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U11(plus(x0, 0), x2, x3)) -> c8(A__U11(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U11(plus(U11(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U11(plus(U12(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U11(plus(plus(z0, z1), x1), x2, x3)) -> c8(A__U11(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U11(plus(tt, x1), x2, x3)) -> c8(A__U11(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U11(plus(s(z0), x1), x2, x3)) -> c8(A__U11(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U11(plus(0, x1), x2, x3)) -> c8(A__U11(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U11(plus(x0, x1), x2, x3)) -> c8(MARK(plus(x0, x1))) MARK(U12(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U12(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U12(U11(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U12(U11(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U12(U11(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U12(U11(x0, z1, z2), x3, x4)) -> c9(MARK(U11(x0, z1, z2))) MARK(U12(U11(0, x1, x2), x3, x4)) -> c9(A__U12(a__U11(0, x1, x2), x3, x4)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_1, c9_2, c9_1, c10_2, c10_1, c11_2, c11_1, c8_2 ---------------------------------------- (157) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U12(U12(z0, z1, z2), x1, x2)) -> c9(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) by MARK(U12(U12(x0, z1, z2), x3, x4)) -> c9(A__U12(U12(mark(x0), z1, z2), x3, x4), MARK(U12(x0, z1, z2))) MARK(U12(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U12(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U12(U12(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U12(U12(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U12(U12(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U12(U12(0, x1, x2), x3, x4)) -> c9(A__U12(a__U12(0, x1, x2), x3, x4), MARK(U12(0, x1, x2))) ---------------------------------------- (158) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 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x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U12(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c3(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c3(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U12(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U12(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U12(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, 0) -> c3(A__PLUS(0, 0)) MARK(U11(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U11(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U11(U11(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U11(U11(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U11(U11(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U11(U11(x0, z1, z2), x3, x4)) -> c8(MARK(U11(x0, z1, z2))) MARK(U11(U11(0, x1, x2), x3, x4)) -> c8(A__U11(a__U11(0, x1, x2), x3, x4)) MARK(U11(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U11(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U11(U12(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U11(U12(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U11(U12(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U11(U12(x0, z1, z2), x3, x4)) -> c8(MARK(U12(x0, z1, z2))) MARK(U11(U12(0, x1, x2), x3, x4)) -> c8(A__U11(a__U12(0, x1, x2), x3, x4)) MARK(U11(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U11(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U11(plus(x0, plus(z0, z1)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U11(plus(x0, tt), x2, x3)) -> c8(A__U11(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U11(plus(x0, s(z0)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U11(plus(x0, 0), x2, x3)) -> c8(A__U11(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U11(plus(U11(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U11(plus(U12(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U11(plus(plus(z0, z1), x1), x2, x3)) -> c8(A__U11(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U11(plus(tt, x1), x2, x3)) -> c8(A__U11(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U11(plus(s(z0), x1), x2, x3)) -> c8(A__U11(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U11(plus(0, x1), x2, x3)) -> c8(A__U11(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U11(plus(x0, x1), x2, x3)) -> c8(MARK(plus(x0, x1))) MARK(U12(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U12(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U12(U11(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U12(U11(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U12(U11(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U12(U11(x0, z1, z2), x3, x4)) -> c9(MARK(U11(x0, z1, z2))) MARK(U12(U11(0, x1, x2), x3, x4)) -> c9(A__U12(a__U11(0, x1, x2), x3, x4)) MARK(U12(U12(x0, z1, z2), x3, x4)) -> c9(A__U12(U12(mark(x0), z1, z2), x3, x4), MARK(U12(x0, z1, z2))) MARK(U12(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U12(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U12(U12(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U12(U12(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U12(U12(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U12(U12(0, x1, x2), x3, x4)) -> c9(A__U12(a__U12(0, x1, x2), x3, x4), MARK(U12(0, x1, x2))) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), 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z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U11(U12(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U11(U12(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U11(U12(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U11(U12(x0, z1, z2), x3, x4)) -> c8(MARK(U12(x0, z1, z2))) MARK(U11(U12(0, x1, x2), x3, x4)) -> c8(A__U11(a__U12(0, x1, x2), x3, x4)) MARK(U11(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U11(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U11(plus(x0, plus(z0, z1)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U11(plus(x0, tt), x2, x3)) -> c8(A__U11(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U11(plus(x0, s(z0)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U11(plus(x0, 0), x2, x3)) -> c8(A__U11(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U11(plus(U11(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U11(plus(U12(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U11(plus(plus(z0, z1), x1), x2, x3)) -> c8(A__U11(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U11(plus(tt, x1), x2, x3)) -> c8(A__U11(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U11(plus(s(z0), x1), x2, x3)) -> c8(A__U11(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U11(plus(0, x1), x2, x3)) -> c8(A__U11(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U11(plus(x0, x1), x2, x3)) -> c8(MARK(plus(x0, x1))) MARK(U12(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U12(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U12(U11(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U12(U11(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U12(U11(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U12(U11(x0, z1, z2), x3, x4)) -> c9(MARK(U11(x0, z1, z2))) MARK(U12(U11(0, x1, x2), x3, x4)) -> c9(A__U12(a__U11(0, x1, x2), x3, x4)) MARK(U12(U12(x0, z1, z2), x3, x4)) -> c9(A__U12(U12(mark(x0), z1, z2), x3, x4), MARK(U12(x0, z1, z2))) MARK(U12(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U12(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U12(U12(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U12(U12(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U12(U12(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U12(U12(0, x1, x2), x3, x4)) -> c9(A__U12(a__U12(0, x1, x2), x3, x4), MARK(U12(0, x1, x2))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_1, c9_2, c9_1, c10_2, c10_1, c11_2, c11_1, c8_2 ---------------------------------------- (159) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (160) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U12(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c3(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c3(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U12(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U12(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U12(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, 0) -> c3(A__PLUS(0, 0)) MARK(U11(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U11(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U11(U11(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U11(U11(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U11(U11(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U11(U11(x0, z1, z2), x3, x4)) -> c8(MARK(U11(x0, z1, z2))) MARK(U11(U11(0, x1, x2), x3, x4)) -> c8(A__U11(a__U11(0, x1, x2), x3, x4)) MARK(U11(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U11(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U11(U12(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U11(U12(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U11(U12(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U11(U12(x0, z1, z2), x3, x4)) -> c8(MARK(U12(x0, z1, z2))) MARK(U11(U12(0, x1, x2), x3, x4)) -> c8(A__U11(a__U12(0, x1, x2), x3, x4)) MARK(U11(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U11(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U11(plus(x0, plus(z0, z1)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U11(plus(x0, tt), x2, x3)) -> c8(A__U11(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U11(plus(x0, s(z0)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U11(plus(x0, 0), x2, x3)) -> c8(A__U11(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U11(plus(U11(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U11(plus(U12(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U11(plus(plus(z0, z1), x1), x2, x3)) -> c8(A__U11(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U11(plus(tt, x1), x2, x3)) -> c8(A__U11(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U11(plus(s(z0), x1), x2, x3)) -> c8(A__U11(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U11(plus(0, x1), x2, x3)) -> c8(A__U11(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U11(plus(x0, x1), x2, x3)) -> c8(MARK(plus(x0, x1))) MARK(U12(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U12(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U12(U11(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U12(U11(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U12(U11(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U12(U11(x0, z1, z2), x3, x4)) -> c9(MARK(U11(x0, z1, z2))) MARK(U12(U11(0, x1, x2), x3, x4)) -> c9(A__U12(a__U11(0, x1, x2), x3, x4)) MARK(U12(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U12(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U12(U12(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U12(U12(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U12(U12(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U12(U12(x0, z1, z2), x3, x4)) -> c9(MARK(U12(x0, z1, z2))) MARK(U12(U12(0, x1, x2), x3, x4)) -> c9(A__U12(a__U12(0, x1, x2), x3, x4)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, 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A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U12(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c3(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c3(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U12(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U12(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U12(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, 0) -> c3(A__PLUS(0, 0)) MARK(U11(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U11(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U11(U11(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U11(U11(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U11(U11(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U11(U11(x0, z1, z2), x3, x4)) -> c8(MARK(U11(x0, z1, z2))) MARK(U11(U11(0, x1, x2), x3, x4)) -> c8(A__U11(a__U11(0, x1, x2), x3, x4)) MARK(U11(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U11(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U11(U12(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U11(U12(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U11(U12(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U11(U12(x0, z1, z2), x3, x4)) -> c8(MARK(U12(x0, z1, z2))) MARK(U11(U12(0, x1, x2), x3, x4)) -> c8(A__U11(a__U12(0, x1, x2), x3, x4)) MARK(U11(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U11(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U11(plus(x0, plus(z0, z1)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U11(plus(x0, tt), x2, x3)) -> c8(A__U11(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U11(plus(x0, s(z0)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U11(plus(x0, 0), x2, x3)) -> c8(A__U11(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U11(plus(U11(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U11(plus(U12(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U11(plus(plus(z0, z1), x1), x2, x3)) -> c8(A__U11(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U11(plus(tt, x1), x2, x3)) -> c8(A__U11(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U11(plus(s(z0), x1), x2, x3)) -> c8(A__U11(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U11(plus(0, x1), x2, x3)) -> c8(A__U11(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U11(plus(x0, x1), x2, x3)) -> c8(MARK(plus(x0, x1))) MARK(U12(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U12(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U12(U11(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U12(U11(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U12(U11(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U12(U11(x0, z1, z2), x3, x4)) -> c9(MARK(U11(x0, z1, z2))) MARK(U12(U11(0, x1, x2), x3, x4)) -> c9(A__U12(a__U11(0, x1, x2), x3, x4)) MARK(U12(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U12(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U12(U12(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U12(U12(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U12(U12(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U12(U12(x0, z1, z2), x3, x4)) -> c9(MARK(U12(x0, z1, z2))) MARK(U12(U12(0, x1, x2), x3, x4)) -> c9(A__U12(a__U12(0, x1, x2), x3, x4)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_1, c9_2, c9_1, c10_2, c10_1, c11_2, c11_1, c8_2 ---------------------------------------- (161) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U12(plus(z0, z1), x1, x2)) -> c9(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) by MARK(U12(plus(x0, x1), x2, x3)) -> c9(A__U12(plus(mark(x0), mark(x1)), x2, x3), MARK(plus(x0, x1))) MARK(U12(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U12(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U12(plus(x0, plus(z0, z1)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U12(plus(x0, tt), x2, x3)) -> c9(A__U12(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U12(plus(x0, s(z0)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U12(plus(x0, 0), x2, x3)) -> c9(A__U12(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U12(plus(U11(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U12(plus(U12(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U12(plus(plus(z0, z1), x1), x2, x3)) -> c9(A__U12(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U12(plus(tt, x1), x2, x3)) -> c9(A__U12(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U12(plus(s(z0), x1), x2, x3)) -> c9(A__U12(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U12(plus(0, x1), x2, x3)) -> c9(A__U12(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) ---------------------------------------- (162) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> 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A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, 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c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U12(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c3(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c3(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U12(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U12(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U12(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, 0) -> c3(A__PLUS(0, 0)) MARK(U11(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U11(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U11(U11(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U11(U11(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U11(U11(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U11(U11(x0, z1, z2), x3, x4)) -> c8(MARK(U11(x0, z1, z2))) MARK(U11(U11(0, x1, x2), x3, x4)) -> c8(A__U11(a__U11(0, x1, x2), x3, x4)) MARK(U11(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U11(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U11(U12(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U11(U12(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U11(U12(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U11(U12(x0, z1, z2), x3, x4)) -> c8(MARK(U12(x0, z1, z2))) MARK(U11(U12(0, x1, x2), x3, x4)) -> c8(A__U11(a__U12(0, x1, x2), x3, x4)) MARK(U11(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U11(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U11(plus(x0, plus(z0, z1)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U11(plus(x0, tt), x2, x3)) -> c8(A__U11(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U11(plus(x0, s(z0)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U11(plus(x0, 0), x2, x3)) -> c8(A__U11(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U11(plus(U11(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U11(plus(U12(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U11(plus(plus(z0, z1), x1), x2, x3)) -> c8(A__U11(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U11(plus(tt, x1), x2, x3)) -> c8(A__U11(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U11(plus(s(z0), x1), x2, x3)) -> c8(A__U11(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U11(plus(0, x1), x2, x3)) -> c8(A__U11(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U11(plus(x0, x1), x2, x3)) -> c8(MARK(plus(x0, x1))) MARK(U12(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U12(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U12(U11(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U12(U11(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U12(U11(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U12(U11(x0, z1, z2), x3, x4)) -> c9(MARK(U11(x0, z1, z2))) MARK(U12(U11(0, x1, x2), x3, x4)) -> c9(A__U12(a__U11(0, x1, x2), x3, x4)) MARK(U12(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U12(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U12(U12(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U12(U12(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U12(U12(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U12(U12(x0, z1, z2), x3, x4)) -> c9(MARK(U12(x0, z1, z2))) MARK(U12(U12(0, x1, x2), x3, x4)) -> c9(A__U12(a__U12(0, x1, x2), x3, x4)) MARK(U12(plus(x0, x1), x2, x3)) -> c9(A__U12(plus(mark(x0), mark(x1)), x2, x3), MARK(plus(x0, x1))) MARK(U12(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U12(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U12(plus(x0, plus(z0, z1)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U12(plus(x0, tt), x2, x3)) -> c9(A__U12(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U12(plus(x0, s(z0)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U12(plus(x0, 0), x2, x3)) -> c9(A__U12(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U12(plus(U11(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U12(plus(U12(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U12(plus(plus(z0, z1), x1), x2, x3)) -> c9(A__U12(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U12(plus(tt, x1), x2, x3)) -> c9(A__U12(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U12(plus(s(z0), x1), x2, x3)) -> c9(A__U12(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U12(plus(0, x1), x2, x3)) -> c9(A__U12(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), 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x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U11(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U11(U11(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U11(U11(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U11(U11(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U11(U11(x0, z1, z2), x3, x4)) -> c8(MARK(U11(x0, z1, z2))) MARK(U11(U11(0, x1, x2), x3, x4)) -> c8(A__U11(a__U11(0, x1, x2), x3, x4)) MARK(U11(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U11(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U11(U12(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U11(U12(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U11(U12(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U11(U12(x0, z1, z2), x3, x4)) -> c8(MARK(U12(x0, z1, z2))) MARK(U11(U12(0, x1, x2), x3, x4)) -> c8(A__U11(a__U12(0, x1, x2), x3, x4)) MARK(U11(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U11(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U11(plus(x0, plus(z0, z1)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U11(plus(x0, tt), x2, x3)) -> c8(A__U11(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U11(plus(x0, s(z0)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U11(plus(x0, 0), x2, x3)) -> c8(A__U11(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U11(plus(U11(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U11(plus(U12(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U11(plus(plus(z0, z1), x1), x2, x3)) -> c8(A__U11(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U11(plus(tt, x1), x2, x3)) -> c8(A__U11(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U11(plus(s(z0), x1), x2, x3)) -> c8(A__U11(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U11(plus(0, x1), x2, x3)) -> c8(A__U11(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U11(plus(x0, x1), x2, x3)) -> c8(MARK(plus(x0, x1))) MARK(U12(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U12(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U12(U11(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U12(U11(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U12(U11(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U12(U11(x0, z1, z2), x3, x4)) -> c9(MARK(U11(x0, z1, z2))) MARK(U12(U11(0, x1, x2), x3, x4)) -> c9(A__U12(a__U11(0, x1, x2), x3, x4)) MARK(U12(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U12(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U12(U12(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U12(U12(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U12(U12(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U12(U12(x0, z1, z2), x3, x4)) -> c9(MARK(U12(x0, z1, z2))) MARK(U12(U12(0, x1, x2), x3, x4)) -> c9(A__U12(a__U12(0, x1, x2), x3, x4)) MARK(U12(plus(x0, x1), x2, x3)) -> c9(A__U12(plus(mark(x0), mark(x1)), x2, x3), MARK(plus(x0, x1))) MARK(U12(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U12(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U12(plus(x0, plus(z0, z1)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U12(plus(x0, tt), x2, x3)) -> c9(A__U12(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U12(plus(x0, s(z0)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U12(plus(x0, 0), x2, x3)) -> c9(A__U12(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U12(plus(U11(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U12(plus(U12(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U12(plus(plus(z0, z1), x1), x2, x3)) -> c9(A__U12(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U12(plus(tt, x1), x2, x3)) -> c9(A__U12(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U12(plus(s(z0), x1), x2, x3)) -> c9(A__U12(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U12(plus(0, x1), x2, x3)) -> c9(A__U12(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_1, c9_1, c10_2, c10_1, c11_2, c11_1, c8_2, c9_2 ---------------------------------------- (163) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (164) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), 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c9(A__U12(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U12(U12(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U12(U12(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U12(U12(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U12(U12(x0, z1, z2), x3, x4)) -> c9(MARK(U12(x0, z1, z2))) MARK(U12(U12(0, x1, x2), x3, x4)) -> c9(A__U12(a__U12(0, x1, x2), x3, x4)) MARK(U12(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U12(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U12(plus(x0, plus(z0, z1)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U12(plus(x0, tt), x2, x3)) -> c9(A__U12(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U12(plus(x0, s(z0)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U12(plus(x0, 0), x2, x3)) -> c9(A__U12(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U12(plus(U11(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U12(plus(U12(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U12(plus(plus(z0, z1), x1), x2, x3)) -> c9(A__U12(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U12(plus(tt, x1), x2, x3)) -> c9(A__U12(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U12(plus(s(z0), x1), x2, x3)) -> c9(A__U12(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U12(plus(0, x1), x2, x3)) -> c9(A__U12(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U12(plus(x0, x1), x2, x3)) -> c9(MARK(plus(x0, x1))) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U12(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c3(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c3(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U12(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U12(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U12(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, 0) -> c3(A__PLUS(0, 0)) MARK(U11(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U11(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U11(U11(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U11(U11(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U11(U11(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U11(U11(x0, z1, z2), x3, x4)) -> c8(MARK(U11(x0, z1, z2))) MARK(U11(U11(0, x1, x2), x3, x4)) -> c8(A__U11(a__U11(0, x1, x2), x3, x4)) MARK(U11(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U11(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U11(U12(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U11(U12(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U11(U12(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U11(U12(x0, z1, z2), x3, x4)) -> c8(MARK(U12(x0, z1, z2))) MARK(U11(U12(0, x1, x2), x3, x4)) -> c8(A__U11(a__U12(0, x1, x2), x3, x4)) MARK(U11(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U11(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U11(plus(x0, plus(z0, z1)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U11(plus(x0, tt), x2, x3)) -> c8(A__U11(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U11(plus(x0, s(z0)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U11(plus(x0, 0), x2, x3)) -> c8(A__U11(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U11(plus(U11(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U11(plus(U12(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U11(plus(plus(z0, z1), x1), x2, x3)) -> c8(A__U11(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U11(plus(tt, x1), x2, x3)) -> c8(A__U11(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U11(plus(s(z0), x1), x2, x3)) -> c8(A__U11(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U11(plus(0, x1), x2, x3)) -> c8(A__U11(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U11(plus(x0, x1), x2, x3)) -> c8(MARK(plus(x0, x1))) MARK(U12(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U12(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U12(U11(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U12(U11(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U12(U11(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U12(U11(x0, z1, z2), x3, x4)) -> c9(MARK(U11(x0, z1, z2))) MARK(U12(U11(0, x1, x2), x3, x4)) -> c9(A__U12(a__U11(0, x1, x2), x3, x4)) MARK(U12(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U12(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U12(U12(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U12(U12(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U12(U12(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U12(U12(x0, z1, z2), x3, x4)) -> c9(MARK(U12(x0, z1, z2))) MARK(U12(U12(0, x1, x2), x3, x4)) -> c9(A__U12(a__U12(0, x1, x2), x3, x4)) MARK(U12(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U12(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U12(plus(x0, plus(z0, z1)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U12(plus(x0, tt), x2, x3)) -> c9(A__U12(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U12(plus(x0, s(z0)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U12(plus(x0, 0), x2, x3)) -> c9(A__U12(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U12(plus(U11(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U12(plus(U12(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U12(plus(plus(z0, z1), x1), x2, x3)) -> c9(A__U12(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U12(plus(tt, x1), x2, x3)) -> c9(A__U12(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U12(plus(s(z0), x1), x2, x3)) -> c9(A__U12(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U12(plus(0, x1), x2, x3)) -> c9(A__U12(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U12(plus(x0, x1), x2, x3)) -> c9(MARK(plus(x0, x1))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_1, c9_1, c10_2, c10_1, c11_2, c11_1, c8_2, c9_2 ---------------------------------------- (165) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(x0, U11(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) by MARK(plus(x0, U11(x1, z1, z2))) -> c10(A__PLUS(mark(x0), U11(mark(x1), z1, z2)), MARK(x0)) MARK(plus(x0, U11(U11(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__U11(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U11(U12(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__U12(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U11(plus(z0, z1), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(tt, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U11(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U11(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(tt, U11(x1, x2, x3))) -> c10(A__PLUS(tt, a__U11(mark(x1), x2, x3)), MARK(tt)) MARK(plus(s(z0), U11(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(0, U11(x1, x2, x3))) -> c10(A__PLUS(0, a__U11(mark(x1), x2, x3)), MARK(0)) ---------------------------------------- (166) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), 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x1))) MARK(U11(plus(s(z0), x1), x2, x3)) -> c8(A__U11(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U11(plus(0, x1), x2, x3)) -> c8(A__U11(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U11(plus(x0, x1), x2, x3)) -> c8(MARK(plus(x0, x1))) MARK(U12(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U12(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U12(U11(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U12(U11(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U12(U11(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U12(U11(x0, z1, z2), x3, x4)) -> c9(MARK(U11(x0, z1, z2))) MARK(U12(U11(0, x1, x2), x3, x4)) -> c9(A__U12(a__U11(0, x1, x2), x3, x4)) MARK(U12(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U12(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U12(U12(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U12(U12(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U12(U12(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U12(U12(x0, z1, z2), x3, x4)) -> c9(MARK(U12(x0, z1, z2))) MARK(U12(U12(0, x1, x2), x3, x4)) -> c9(A__U12(a__U12(0, x1, x2), x3, x4)) MARK(U12(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U12(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U12(plus(x0, plus(z0, z1)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U12(plus(x0, tt), x2, x3)) -> c9(A__U12(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U12(plus(x0, s(z0)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U12(plus(x0, 0), x2, x3)) -> c9(A__U12(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U12(plus(U11(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U12(plus(U12(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U12(plus(plus(z0, z1), x1), x2, x3)) -> c9(A__U12(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U12(plus(tt, x1), x2, x3)) -> c9(A__U12(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U12(plus(s(z0), x1), x2, x3)) -> c9(A__U12(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U12(plus(0, x1), x2, x3)) -> c9(A__U12(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U12(plus(x0, x1), x2, x3)) -> c9(MARK(plus(x0, x1))) MARK(plus(x0, U11(x1, z1, z2))) -> c10(A__PLUS(mark(x0), U11(mark(x1), z1, z2)), MARK(x0)) MARK(plus(x0, U11(U11(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__U11(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U11(U12(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__U12(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U11(plus(z0, z1), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(tt, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U11(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U11(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(tt, U11(x1, x2, x3))) -> c10(A__PLUS(tt, a__U11(mark(x1), x2, x3)), MARK(tt)) MARK(plus(s(z0), U11(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(0, U11(x1, x2, x3))) -> c10(A__PLUS(0, a__U11(mark(x1), x2, x3)), MARK(0)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), 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U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U12(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c3(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c3(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U12(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U12(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U12(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, 0) -> c3(A__PLUS(0, 0)) MARK(U11(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U11(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U11(U11(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U11(U11(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U11(U11(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U11(U11(x0, z1, z2), x3, x4)) -> c8(MARK(U11(x0, z1, z2))) MARK(U11(U11(0, x1, x2), x3, x4)) -> c8(A__U11(a__U11(0, x1, x2), x3, x4)) MARK(U11(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U11(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U11(U12(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U11(U12(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U11(U12(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U11(U12(x0, z1, z2), x3, x4)) -> c8(MARK(U12(x0, z1, z2))) MARK(U11(U12(0, x1, x2), x3, x4)) -> c8(A__U11(a__U12(0, x1, x2), x3, x4)) MARK(U11(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U11(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U11(plus(x0, plus(z0, z1)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U11(plus(x0, tt), x2, x3)) -> c8(A__U11(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U11(plus(x0, s(z0)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U11(plus(x0, 0), x2, x3)) -> c8(A__U11(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U11(plus(U11(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U11(plus(U12(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U11(plus(plus(z0, z1), x1), x2, x3)) -> c8(A__U11(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U11(plus(tt, x1), x2, x3)) -> c8(A__U11(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U11(plus(s(z0), x1), x2, x3)) -> c8(A__U11(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U11(plus(0, x1), x2, x3)) -> c8(A__U11(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U11(plus(x0, x1), x2, x3)) -> c8(MARK(plus(x0, x1))) MARK(U12(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U12(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U12(U11(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U12(U11(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U12(U11(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U12(U11(x0, z1, z2), x3, x4)) -> c9(MARK(U11(x0, z1, z2))) MARK(U12(U11(0, x1, x2), x3, x4)) -> c9(A__U12(a__U11(0, x1, x2), x3, x4)) MARK(U12(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U12(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U12(U12(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U12(U12(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U12(U12(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U12(U12(x0, z1, z2), x3, x4)) -> c9(MARK(U12(x0, z1, z2))) MARK(U12(U12(0, x1, x2), x3, x4)) -> c9(A__U12(a__U12(0, x1, x2), x3, x4)) MARK(U12(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U12(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U12(plus(x0, plus(z0, z1)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U12(plus(x0, tt), x2, x3)) -> c9(A__U12(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U12(plus(x0, s(z0)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U12(plus(x0, 0), x2, x3)) -> c9(A__U12(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U12(plus(U11(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U12(plus(U12(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U12(plus(plus(z0, z1), x1), x2, x3)) -> c9(A__U12(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U12(plus(tt, x1), x2, x3)) -> c9(A__U12(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U12(plus(s(z0), x1), x2, x3)) -> c9(A__U12(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U12(plus(0, x1), x2, x3)) -> c9(A__U12(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U12(plus(x0, x1), x2, x3)) -> c9(MARK(plus(x0, x1))) MARK(plus(x0, U11(x1, z1, z2))) -> c10(A__PLUS(mark(x0), U11(mark(x1), z1, z2)), MARK(x0)) MARK(plus(x0, U11(U11(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__U11(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U11(U12(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__U12(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U11(plus(z0, z1), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(tt, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U11(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U11(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(tt, U11(x1, x2, x3))) -> c10(A__PLUS(tt, a__U11(mark(x1), x2, x3)), MARK(tt)) MARK(plus(s(z0), U11(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(0, U11(x1, x2, x3))) -> c10(A__PLUS(0, a__U11(mark(x1), x2, x3)), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_1, c9_1, c10_2, c10_1, c11_2, c11_1, c8_2, c9_2 ---------------------------------------- (167) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (168) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> 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A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U12(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c3(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c3(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U12(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U12(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U12(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, 0) -> c3(A__PLUS(0, 0)) MARK(U11(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U11(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U11(U11(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U11(U11(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U11(U11(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U11(U11(x0, z1, z2), x3, x4)) -> c8(MARK(U11(x0, z1, z2))) MARK(U11(U11(0, x1, x2), x3, x4)) -> c8(A__U11(a__U11(0, x1, x2), x3, x4)) MARK(U11(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U11(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U11(U12(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U11(U12(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U11(U12(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U11(U12(x0, z1, z2), x3, x4)) -> c8(MARK(U12(x0, z1, z2))) MARK(U11(U12(0, x1, x2), x3, x4)) -> c8(A__U11(a__U12(0, x1, x2), x3, x4)) MARK(U11(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U11(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U11(plus(x0, plus(z0, z1)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U11(plus(x0, tt), x2, x3)) -> c8(A__U11(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U11(plus(x0, s(z0)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U11(plus(x0, 0), x2, x3)) -> c8(A__U11(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U11(plus(U11(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U11(plus(U12(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U11(plus(plus(z0, z1), x1), x2, x3)) -> c8(A__U11(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U11(plus(tt, x1), x2, x3)) -> c8(A__U11(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U11(plus(s(z0), x1), x2, x3)) -> c8(A__U11(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U11(plus(0, x1), x2, x3)) -> c8(A__U11(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U11(plus(x0, x1), x2, x3)) -> c8(MARK(plus(x0, x1))) MARK(U12(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U12(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U12(U11(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U12(U11(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U12(U11(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U12(U11(x0, z1, z2), x3, x4)) -> c9(MARK(U11(x0, z1, z2))) MARK(U12(U11(0, x1, x2), x3, x4)) -> c9(A__U12(a__U11(0, x1, x2), x3, x4)) MARK(U12(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U12(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U12(U12(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U12(U12(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U12(U12(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U12(U12(x0, z1, z2), x3, x4)) -> c9(MARK(U12(x0, z1, z2))) MARK(U12(U12(0, x1, x2), x3, x4)) -> c9(A__U12(a__U12(0, x1, x2), x3, x4)) MARK(U12(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U12(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U12(plus(x0, plus(z0, z1)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U12(plus(x0, tt), x2, x3)) -> c9(A__U12(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U12(plus(x0, s(z0)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U12(plus(x0, 0), x2, x3)) -> c9(A__U12(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U12(plus(U11(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U12(plus(U12(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U12(plus(plus(z0, z1), x1), x2, x3)) -> c9(A__U12(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U12(plus(tt, x1), x2, x3)) -> c9(A__U12(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U12(plus(s(z0), x1), x2, x3)) -> c9(A__U12(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U12(plus(0, x1), x2, x3)) -> c9(A__U12(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U12(plus(x0, x1), x2, x3)) -> c9(MARK(plus(x0, x1))) MARK(plus(x0, U11(U11(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__U11(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U11(U12(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__U12(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U11(plus(z0, z1), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(tt, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U11(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U11(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(s(z0), U11(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(x0, U11(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U11(x1, x2, x3))) -> c10(A__PLUS(tt, a__U11(mark(x1), x2, x3))) MARK(plus(0, U11(x1, x2, x3))) -> c10(A__PLUS(0, a__U11(mark(x1), x2, x3))) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), 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MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), 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c8(A__U11(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U11(U12(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U11(U12(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U11(U12(x0, z1, z2), x3, x4)) -> c8(MARK(U12(x0, z1, z2))) MARK(U11(U12(0, x1, x2), x3, x4)) -> c8(A__U11(a__U12(0, x1, x2), x3, x4)) MARK(U11(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U11(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U11(plus(x0, plus(z0, z1)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U11(plus(x0, tt), x2, x3)) -> c8(A__U11(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U11(plus(x0, s(z0)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U11(plus(x0, 0), x2, x3)) -> c8(A__U11(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U11(plus(U11(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U11(plus(U12(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U11(plus(plus(z0, z1), x1), x2, x3)) -> c8(A__U11(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U11(plus(tt, x1), x2, x3)) -> c8(A__U11(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U11(plus(s(z0), x1), x2, x3)) -> c8(A__U11(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U11(plus(0, x1), x2, x3)) -> c8(A__U11(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U11(plus(x0, x1), x2, x3)) -> c8(MARK(plus(x0, x1))) MARK(U12(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U12(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U12(U11(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U12(U11(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U12(U11(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U12(U11(x0, z1, z2), x3, x4)) -> c9(MARK(U11(x0, z1, z2))) MARK(U12(U11(0, x1, x2), x3, x4)) -> c9(A__U12(a__U11(0, x1, x2), x3, x4)) MARK(U12(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U12(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U12(U12(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U12(U12(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U12(U12(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U12(U12(x0, z1, z2), x3, x4)) -> c9(MARK(U12(x0, z1, z2))) MARK(U12(U12(0, x1, x2), x3, x4)) -> c9(A__U12(a__U12(0, x1, x2), x3, x4)) MARK(U12(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U12(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U12(plus(x0, plus(z0, z1)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U12(plus(x0, tt), x2, x3)) -> c9(A__U12(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U12(plus(x0, s(z0)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U12(plus(x0, 0), x2, x3)) -> c9(A__U12(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U12(plus(U11(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U12(plus(U12(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U12(plus(plus(z0, z1), x1), x2, x3)) -> c9(A__U12(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U12(plus(tt, x1), x2, x3)) -> c9(A__U12(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U12(plus(s(z0), x1), x2, x3)) -> c9(A__U12(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U12(plus(0, x1), x2, x3)) -> c9(A__U12(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U12(plus(x0, x1), x2, x3)) -> c9(MARK(plus(x0, x1))) MARK(plus(x0, U11(U11(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__U11(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U11(U12(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__U12(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U11(plus(z0, z1), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(tt, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U11(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U11(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(s(z0), U11(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(x0, U11(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U11(x1, x2, x3))) -> c10(A__PLUS(tt, a__U11(mark(x1), x2, x3))) MARK(plus(0, U11(x1, x2, x3))) -> c10(A__PLUS(0, a__U11(mark(x1), x2, x3))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_1, c9_1, c10_2, c10_1, c11_2, c11_1, c8_2, c9_2 ---------------------------------------- (169) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(x0, U12(z0, z1, z2))) -> c10(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) by MARK(plus(x0, U12(x1, z1, z2))) -> c10(A__PLUS(mark(x0), U12(mark(x1), z1, z2)), MARK(x0)) MARK(plus(x0, U12(U11(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__U11(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U12(U12(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__U12(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U12(plus(z0, z1), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(x0)) MARK(plus(x0, U12(tt, x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U12(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U12(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U12(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U12(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U12(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(tt, U12(x1, x2, x3))) -> c10(A__PLUS(tt, a__U12(mark(x1), x2, x3)), MARK(tt)) MARK(plus(s(z0), U12(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(0, U12(x1, x2, x3))) -> c10(A__PLUS(0, a__U12(mark(x1), x2, x3)), MARK(0)) ---------------------------------------- (170) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> 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c9(A__U12(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U12(U12(x0, z1, z2), x3, x4)) -> c9(MARK(U12(x0, z1, z2))) MARK(U12(U12(0, x1, x2), x3, x4)) -> c9(A__U12(a__U12(0, x1, x2), x3, x4)) MARK(U12(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U12(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U12(plus(x0, plus(z0, z1)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U12(plus(x0, tt), x2, x3)) -> c9(A__U12(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U12(plus(x0, s(z0)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U12(plus(x0, 0), x2, x3)) -> c9(A__U12(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U12(plus(U11(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U12(plus(U12(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U12(plus(plus(z0, z1), x1), x2, x3)) -> c9(A__U12(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U12(plus(tt, x1), x2, x3)) -> c9(A__U12(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U12(plus(s(z0), x1), x2, x3)) -> c9(A__U12(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U12(plus(0, x1), x2, x3)) -> c9(A__U12(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U12(plus(x0, x1), x2, x3)) -> c9(MARK(plus(x0, x1))) MARK(plus(x0, U11(U11(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__U11(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U11(U12(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__U12(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U11(plus(z0, z1), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(tt, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U11(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U11(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(s(z0), U11(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(x0, U11(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U11(x1, x2, x3))) -> c10(A__PLUS(tt, a__U11(mark(x1), x2, x3))) MARK(plus(0, U11(x1, x2, x3))) -> c10(A__PLUS(0, a__U11(mark(x1), x2, x3))) MARK(plus(x0, U12(x1, z1, z2))) -> c10(A__PLUS(mark(x0), U12(mark(x1), z1, z2)), MARK(x0)) MARK(plus(x0, U12(U11(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__U11(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U12(U12(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__U12(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U12(plus(z0, z1), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(x0)) MARK(plus(x0, U12(tt, x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U12(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U12(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U12(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U12(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U12(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(tt, U12(x1, x2, x3))) -> c10(A__PLUS(tt, a__U12(mark(x1), x2, x3)), MARK(tt)) MARK(plus(s(z0), U12(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(0, U12(x1, x2, x3))) -> c10(A__PLUS(0, a__U12(mark(x1), x2, x3)), MARK(0)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> 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U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, 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A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, 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c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), 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MARK(plus(x0, U12(z0, z1, z2)))) MARK(U12(plus(x0, plus(z0, z1)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U12(plus(x0, tt), x2, x3)) -> c9(A__U12(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U12(plus(x0, s(z0)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U12(plus(x0, 0), x2, x3)) -> c9(A__U12(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U12(plus(U11(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U12(plus(U12(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U12(plus(plus(z0, z1), x1), x2, x3)) -> c9(A__U12(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U12(plus(tt, x1), x2, x3)) -> c9(A__U12(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U12(plus(s(z0), x1), x2, x3)) -> c9(A__U12(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U12(plus(0, x1), x2, x3)) -> c9(A__U12(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U12(plus(x0, x1), x2, x3)) -> c9(MARK(plus(x0, x1))) MARK(plus(x0, U11(U11(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__U11(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U11(U12(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__U12(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U11(plus(z0, z1), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(tt, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U11(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U11(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(s(z0), U11(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(x0, U11(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U11(x1, x2, x3))) -> c10(A__PLUS(tt, a__U11(mark(x1), x2, x3))) MARK(plus(0, U11(x1, x2, x3))) -> c10(A__PLUS(0, a__U11(mark(x1), x2, x3))) MARK(plus(x0, U12(x1, z1, z2))) -> c10(A__PLUS(mark(x0), U12(mark(x1), z1, z2)), MARK(x0)) MARK(plus(x0, U12(U11(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__U11(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U12(U12(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__U12(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U12(plus(z0, z1), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(x0)) MARK(plus(x0, U12(tt, x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U12(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U12(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U12(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U12(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U12(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(tt, U12(x1, x2, x3))) -> c10(A__PLUS(tt, a__U12(mark(x1), x2, x3)), MARK(tt)) MARK(plus(s(z0), U12(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(0, U12(x1, x2, x3))) -> c10(A__PLUS(0, a__U12(mark(x1), x2, x3)), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_1, c9_1, c10_2, c10_1, c11_2, c11_1, c8_2, c9_2 ---------------------------------------- (171) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (172) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U12(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c3(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c3(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U12(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U12(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U12(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, 0) -> c3(A__PLUS(0, 0)) MARK(U11(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U11(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U11(U11(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U11(U11(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U11(U11(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U11(U11(x0, z1, z2), x3, x4)) -> c8(MARK(U11(x0, z1, z2))) MARK(U11(U11(0, x1, x2), x3, x4)) -> c8(A__U11(a__U11(0, x1, x2), x3, x4)) MARK(U11(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U11(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U11(U12(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U11(U12(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U11(U12(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U11(U12(x0, z1, z2), x3, x4)) -> c8(MARK(U12(x0, z1, z2))) MARK(U11(U12(0, x1, x2), x3, x4)) -> c8(A__U11(a__U12(0, x1, x2), x3, x4)) MARK(U11(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U11(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U11(plus(x0, plus(z0, z1)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U11(plus(x0, tt), x2, x3)) -> c8(A__U11(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U11(plus(x0, s(z0)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U11(plus(x0, 0), x2, x3)) -> c8(A__U11(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U11(plus(U11(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U11(plus(U12(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U11(plus(plus(z0, z1), x1), x2, x3)) -> c8(A__U11(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U11(plus(tt, x1), x2, x3)) -> c8(A__U11(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U11(plus(s(z0), x1), x2, x3)) -> c8(A__U11(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U11(plus(0, x1), x2, x3)) -> c8(A__U11(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U11(plus(x0, x1), x2, x3)) -> c8(MARK(plus(x0, x1))) MARK(U12(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U12(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U12(U11(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U12(U11(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U12(U11(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U12(U11(x0, z1, z2), x3, x4)) -> c9(MARK(U11(x0, z1, z2))) MARK(U12(U11(0, x1, x2), x3, x4)) -> c9(A__U12(a__U11(0, x1, x2), x3, x4)) MARK(U12(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U12(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U12(U12(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U12(U12(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U12(U12(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U12(U12(x0, z1, z2), x3, x4)) -> c9(MARK(U12(x0, z1, z2))) MARK(U12(U12(0, x1, x2), x3, x4)) -> c9(A__U12(a__U12(0, x1, x2), x3, x4)) MARK(U12(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U12(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U12(plus(x0, plus(z0, z1)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U12(plus(x0, tt), x2, x3)) -> c9(A__U12(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U12(plus(x0, s(z0)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U12(plus(x0, 0), x2, x3)) -> c9(A__U12(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U12(plus(U11(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U12(plus(U12(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U12(plus(plus(z0, z1), x1), x2, x3)) -> c9(A__U12(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U12(plus(tt, x1), x2, x3)) -> c9(A__U12(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U12(plus(s(z0), x1), x2, x3)) -> c9(A__U12(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U12(plus(0, x1), x2, x3)) -> c9(A__U12(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U12(plus(x0, x1), x2, x3)) -> c9(MARK(plus(x0, x1))) MARK(plus(x0, U11(U11(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__U11(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U11(U12(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__U12(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U11(plus(z0, z1), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(tt, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U11(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U11(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(s(z0), U11(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(x0, U11(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U11(x1, x2, x3))) -> c10(A__PLUS(tt, a__U11(mark(x1), x2, x3))) MARK(plus(0, U11(x1, x2, x3))) -> c10(A__PLUS(0, a__U11(mark(x1), x2, x3))) MARK(plus(x0, U12(U11(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__U11(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U12(U12(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__U12(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U12(plus(z0, z1), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(x0)) MARK(plus(x0, U12(tt, x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U12(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U12(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U12(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U12(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U12(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(s(z0), U12(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(x0, U12(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U12(x1, x2, x3))) -> c10(A__PLUS(tt, a__U12(mark(x1), x2, x3))) MARK(plus(0, U12(x1, x2, x3))) -> c10(A__PLUS(0, a__U12(mark(x1), x2, x3))) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U12(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c3(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c3(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U12(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U12(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U12(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, 0) -> c3(A__PLUS(0, 0)) MARK(U11(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U11(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U11(U11(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U11(U11(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U11(U11(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U11(U11(x0, z1, z2), x3, x4)) -> c8(MARK(U11(x0, z1, z2))) MARK(U11(U11(0, x1, x2), x3, x4)) -> c8(A__U11(a__U11(0, x1, x2), x3, x4)) MARK(U11(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U11(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U11(U12(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U11(U12(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U11(U12(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U11(U12(x0, z1, z2), x3, x4)) -> c8(MARK(U12(x0, z1, z2))) MARK(U11(U12(0, x1, x2), x3, x4)) -> c8(A__U11(a__U12(0, x1, x2), x3, x4)) MARK(U11(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U11(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U11(plus(x0, plus(z0, z1)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U11(plus(x0, tt), x2, x3)) -> c8(A__U11(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U11(plus(x0, s(z0)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U11(plus(x0, 0), x2, x3)) -> c8(A__U11(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U11(plus(U11(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U11(plus(U12(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U11(plus(plus(z0, z1), x1), x2, x3)) -> c8(A__U11(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U11(plus(tt, x1), x2, x3)) -> c8(A__U11(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U11(plus(s(z0), x1), x2, x3)) -> c8(A__U11(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U11(plus(0, x1), x2, x3)) -> c8(A__U11(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U11(plus(x0, x1), x2, x3)) -> c8(MARK(plus(x0, x1))) MARK(U12(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U12(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U12(U11(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U12(U11(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U12(U11(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U12(U11(x0, z1, z2), x3, x4)) -> c9(MARK(U11(x0, z1, z2))) MARK(U12(U11(0, x1, x2), x3, x4)) -> c9(A__U12(a__U11(0, x1, x2), x3, x4)) MARK(U12(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U12(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U12(U12(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U12(U12(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U12(U12(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U12(U12(x0, z1, z2), x3, x4)) -> c9(MARK(U12(x0, z1, z2))) MARK(U12(U12(0, x1, x2), x3, x4)) -> c9(A__U12(a__U12(0, x1, x2), x3, x4)) MARK(U12(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U12(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U12(plus(x0, plus(z0, z1)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U12(plus(x0, tt), x2, x3)) -> c9(A__U12(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U12(plus(x0, s(z0)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U12(plus(x0, 0), x2, x3)) -> c9(A__U12(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U12(plus(U11(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U12(plus(U12(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U12(plus(plus(z0, z1), x1), x2, x3)) -> c9(A__U12(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U12(plus(tt, x1), x2, x3)) -> c9(A__U12(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U12(plus(s(z0), x1), x2, x3)) -> c9(A__U12(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U12(plus(0, x1), x2, x3)) -> c9(A__U12(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U12(plus(x0, x1), x2, x3)) -> c9(MARK(plus(x0, x1))) MARK(plus(x0, U11(U11(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__U11(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U11(U12(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__U12(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U11(plus(z0, z1), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(tt, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U11(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U11(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(s(z0), U11(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(x0, U11(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U11(x1, x2, x3))) -> c10(A__PLUS(tt, a__U11(mark(x1), x2, x3))) MARK(plus(0, U11(x1, x2, x3))) -> c10(A__PLUS(0, a__U11(mark(x1), x2, x3))) MARK(plus(x0, U12(U11(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__U11(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U12(U12(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__U12(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U12(plus(z0, z1), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(x0)) MARK(plus(x0, U12(tt, x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U12(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U12(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U12(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U12(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U12(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(s(z0), U12(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(x0, U12(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U12(x1, x2, x3))) -> c10(A__PLUS(tt, a__U12(mark(x1), x2, x3))) MARK(plus(0, U12(x1, x2, x3))) -> c10(A__PLUS(0, a__U12(mark(x1), x2, x3))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_1, c9_1, c10_2, c10_1, c11_2, c11_1, c8_2, c9_2 ---------------------------------------- (173) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(x0, plus(z0, z1))) -> c10(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) by MARK(plus(x0, plus(x1, x2))) -> c10(A__PLUS(mark(x0), plus(mark(x1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(x1, U11(z0, z1, z2)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__U11(mark(z0), z1, z2))), MARK(x0)) MARK(plus(x0, plus(x1, U12(z0, z1, z2)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__U12(mark(z0), z1, z2))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(U11(z0, z1, z2), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__U11(mark(z0), z1, z2), mark(x2))), MARK(x0)) MARK(plus(x0, plus(U12(z0, z1, z2), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__U12(mark(z0), z1, z2), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c10(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c10(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c10(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(U11(z0, z1, z2), plus(x1, x2))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), plus(x1, x2))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(tt, plus(x1, x2))) -> c10(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(tt)) MARK(plus(s(z0), plus(x1, x2))) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(0, plus(x1, x2))) -> c10(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(0)) ---------------------------------------- (174) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U12(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c3(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c3(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U12(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U12(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U12(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, 0) -> c3(A__PLUS(0, 0)) MARK(U11(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U11(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U11(U11(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U11(U11(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U11(U11(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U11(U11(x0, z1, z2), x3, x4)) -> c8(MARK(U11(x0, z1, z2))) MARK(U11(U11(0, x1, x2), x3, x4)) -> c8(A__U11(a__U11(0, x1, x2), x3, x4)) MARK(U11(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U11(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U11(U12(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U11(U12(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U11(U12(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U11(U12(x0, z1, z2), x3, x4)) -> c8(MARK(U12(x0, z1, z2))) MARK(U11(U12(0, x1, x2), x3, x4)) -> c8(A__U11(a__U12(0, x1, x2), x3, x4)) MARK(U11(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U11(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U11(plus(x0, plus(z0, z1)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U11(plus(x0, tt), x2, x3)) -> c8(A__U11(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U11(plus(x0, s(z0)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U11(plus(x0, 0), x2, x3)) -> c8(A__U11(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U11(plus(U11(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U11(plus(U12(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U11(plus(plus(z0, z1), x1), x2, x3)) -> c8(A__U11(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U11(plus(tt, x1), x2, x3)) -> c8(A__U11(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U11(plus(s(z0), x1), x2, x3)) -> c8(A__U11(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U11(plus(0, x1), x2, x3)) -> c8(A__U11(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U11(plus(x0, x1), x2, x3)) -> c8(MARK(plus(x0, x1))) MARK(U12(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U12(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U12(U11(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U12(U11(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U12(U11(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U12(U11(x0, z1, z2), x3, x4)) -> c9(MARK(U11(x0, z1, z2))) MARK(U12(U11(0, x1, x2), x3, x4)) -> c9(A__U12(a__U11(0, x1, x2), x3, x4)) MARK(U12(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U12(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U12(U12(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U12(U12(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U12(U12(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U12(U12(x0, z1, z2), x3, x4)) -> c9(MARK(U12(x0, z1, z2))) MARK(U12(U12(0, x1, x2), x3, x4)) -> c9(A__U12(a__U12(0, x1, x2), x3, x4)) MARK(U12(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U12(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U12(plus(x0, plus(z0, z1)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U12(plus(x0, tt), x2, x3)) -> c9(A__U12(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U12(plus(x0, s(z0)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U12(plus(x0, 0), x2, x3)) -> c9(A__U12(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U12(plus(U11(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U12(plus(U12(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U12(plus(plus(z0, z1), x1), x2, x3)) -> c9(A__U12(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U12(plus(tt, x1), x2, x3)) -> c9(A__U12(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U12(plus(s(z0), x1), x2, x3)) -> c9(A__U12(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U12(plus(0, x1), x2, x3)) -> c9(A__U12(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U12(plus(x0, x1), x2, x3)) -> c9(MARK(plus(x0, x1))) MARK(plus(x0, U11(U11(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__U11(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U11(U12(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__U12(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U11(plus(z0, z1), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(tt, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U11(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U11(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(s(z0), U11(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(x0, U11(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U11(x1, x2, x3))) -> c10(A__PLUS(tt, a__U11(mark(x1), x2, x3))) MARK(plus(0, U11(x1, x2, x3))) -> c10(A__PLUS(0, a__U11(mark(x1), x2, x3))) MARK(plus(x0, U12(U11(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__U11(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U12(U12(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__U12(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U12(plus(z0, z1), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(x0)) MARK(plus(x0, U12(tt, x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U12(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U12(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U12(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U12(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U12(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(s(z0), U12(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(x0, U12(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U12(x1, x2, x3))) -> c10(A__PLUS(tt, a__U12(mark(x1), x2, x3))) MARK(plus(0, U12(x1, x2, x3))) -> c10(A__PLUS(0, a__U12(mark(x1), x2, x3))) MARK(plus(x0, plus(x1, x2))) -> c10(A__PLUS(mark(x0), plus(mark(x1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(x1, U11(z0, z1, z2)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__U11(mark(z0), z1, z2))), MARK(x0)) MARK(plus(x0, plus(x1, U12(z0, z1, z2)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__U12(mark(z0), z1, z2))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(U11(z0, z1, z2), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__U11(mark(z0), z1, z2), mark(x2))), MARK(x0)) MARK(plus(x0, plus(U12(z0, z1, z2), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__U12(mark(z0), z1, z2), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c10(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c10(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c10(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(U11(z0, z1, z2), plus(x1, x2))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), plus(x1, x2))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(tt, plus(x1, x2))) -> c10(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(tt)) MARK(plus(s(z0), plus(x1, x2))) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(0, plus(x1, x2))) -> c10(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(0)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) 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MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), 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z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U11(U12(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U11(U12(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U11(U12(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U11(U12(x0, z1, z2), x3, x4)) -> c8(MARK(U12(x0, z1, z2))) MARK(U11(U12(0, x1, x2), x3, x4)) -> c8(A__U11(a__U12(0, x1, x2), x3, x4)) MARK(U11(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U11(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U11(plus(x0, plus(z0, z1)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U11(plus(x0, tt), x2, x3)) -> c8(A__U11(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U11(plus(x0, s(z0)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U11(plus(x0, 0), x2, x3)) -> c8(A__U11(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U11(plus(U11(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U11(plus(U12(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U11(plus(plus(z0, z1), x1), x2, x3)) -> c8(A__U11(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U11(plus(tt, x1), x2, x3)) -> c8(A__U11(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U11(plus(s(z0), x1), x2, x3)) -> c8(A__U11(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U11(plus(0, x1), x2, x3)) -> c8(A__U11(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U11(plus(x0, x1), x2, x3)) -> c8(MARK(plus(x0, x1))) MARK(U12(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U12(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U12(U11(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U12(U11(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U12(U11(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U12(U11(x0, z1, z2), x3, x4)) -> c9(MARK(U11(x0, z1, z2))) MARK(U12(U11(0, x1, x2), x3, x4)) -> c9(A__U12(a__U11(0, x1, x2), x3, x4)) MARK(U12(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U12(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U12(U12(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U12(U12(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U12(U12(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U12(U12(x0, z1, z2), x3, x4)) -> c9(MARK(U12(x0, z1, z2))) MARK(U12(U12(0, x1, x2), x3, x4)) -> c9(A__U12(a__U12(0, x1, x2), x3, x4)) MARK(U12(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U12(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U12(plus(x0, plus(z0, z1)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U12(plus(x0, tt), x2, x3)) -> c9(A__U12(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U12(plus(x0, s(z0)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U12(plus(x0, 0), x2, x3)) -> c9(A__U12(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U12(plus(U11(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U12(plus(U12(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U12(plus(plus(z0, z1), x1), x2, x3)) -> c9(A__U12(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U12(plus(tt, x1), x2, x3)) -> c9(A__U12(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U12(plus(s(z0), x1), x2, x3)) -> c9(A__U12(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U12(plus(0, x1), x2, x3)) -> c9(A__U12(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U12(plus(x0, x1), x2, x3)) -> c9(MARK(plus(x0, x1))) MARK(plus(x0, U11(U11(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__U11(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U11(U12(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__U12(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U11(plus(z0, z1), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(tt, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U11(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U11(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(s(z0), U11(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(x0, U11(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U11(x1, x2, x3))) -> c10(A__PLUS(tt, a__U11(mark(x1), x2, x3))) MARK(plus(0, U11(x1, x2, x3))) -> c10(A__PLUS(0, a__U11(mark(x1), x2, x3))) MARK(plus(x0, U12(U11(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__U11(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U12(U12(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__U12(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U12(plus(z0, z1), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(x0)) MARK(plus(x0, U12(tt, x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U12(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U12(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U12(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U12(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U12(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(s(z0), U12(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(x0, U12(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U12(x1, x2, x3))) -> c10(A__PLUS(tt, a__U12(mark(x1), x2, x3))) MARK(plus(0, U12(x1, x2, x3))) -> c10(A__PLUS(0, a__U12(mark(x1), x2, x3))) MARK(plus(x0, plus(x1, x2))) -> c10(A__PLUS(mark(x0), plus(mark(x1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(x1, U11(z0, z1, z2)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__U11(mark(z0), z1, z2))), MARK(x0)) MARK(plus(x0, plus(x1, U12(z0, z1, z2)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__U12(mark(z0), z1, z2))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(U11(z0, z1, z2), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__U11(mark(z0), z1, z2), mark(x2))), MARK(x0)) MARK(plus(x0, plus(U12(z0, z1, z2), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__U12(mark(z0), z1, z2), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c10(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c10(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c10(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(U11(z0, z1, z2), plus(x1, x2))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), plus(x1, x2))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(tt, plus(x1, x2))) -> c10(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(tt)) MARK(plus(s(z0), plus(x1, x2))) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(0, plus(x1, x2))) -> c10(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_1, c9_1, c10_2, c10_1, c11_2, c11_1, c8_2, c9_2 ---------------------------------------- (175) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (176) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U12(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c3(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c3(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U12(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U12(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U12(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, 0) -> c3(A__PLUS(0, 0)) MARK(U11(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U11(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U11(U11(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U11(U11(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U11(U11(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U11(U11(x0, z1, z2), x3, x4)) -> c8(MARK(U11(x0, z1, z2))) MARK(U11(U11(0, x1, x2), x3, x4)) -> c8(A__U11(a__U11(0, x1, x2), x3, x4)) MARK(U11(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U11(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U11(U12(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U11(U12(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U11(U12(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U11(U12(x0, z1, z2), x3, x4)) -> c8(MARK(U12(x0, z1, z2))) MARK(U11(U12(0, x1, x2), x3, x4)) -> c8(A__U11(a__U12(0, x1, x2), x3, x4)) MARK(U11(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U11(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U11(plus(x0, plus(z0, z1)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U11(plus(x0, tt), x2, x3)) -> c8(A__U11(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U11(plus(x0, s(z0)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U11(plus(x0, 0), x2, x3)) -> c8(A__U11(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U11(plus(U11(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U11(plus(U12(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U11(plus(plus(z0, z1), x1), x2, x3)) -> c8(A__U11(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U11(plus(tt, x1), x2, x3)) -> c8(A__U11(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U11(plus(s(z0), x1), x2, x3)) -> c8(A__U11(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U11(plus(0, x1), x2, x3)) -> c8(A__U11(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U11(plus(x0, x1), x2, x3)) -> c8(MARK(plus(x0, x1))) MARK(U12(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U12(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U12(U11(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U12(U11(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U12(U11(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U12(U11(x0, z1, z2), x3, x4)) -> c9(MARK(U11(x0, z1, z2))) MARK(U12(U11(0, x1, x2), x3, x4)) -> c9(A__U12(a__U11(0, x1, x2), x3, x4)) MARK(U12(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U12(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U12(U12(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U12(U12(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U12(U12(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U12(U12(x0, z1, z2), x3, x4)) -> c9(MARK(U12(x0, z1, z2))) MARK(U12(U12(0, x1, x2), x3, x4)) -> c9(A__U12(a__U12(0, x1, x2), x3, x4)) MARK(U12(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U12(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U12(plus(x0, plus(z0, z1)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U12(plus(x0, tt), x2, x3)) -> c9(A__U12(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U12(plus(x0, s(z0)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U12(plus(x0, 0), x2, x3)) -> c9(A__U12(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U12(plus(U11(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U12(plus(U12(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U12(plus(plus(z0, z1), x1), x2, x3)) -> c9(A__U12(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U12(plus(tt, x1), x2, x3)) -> c9(A__U12(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U12(plus(s(z0), x1), x2, x3)) -> c9(A__U12(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U12(plus(0, x1), x2, x3)) -> c9(A__U12(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U12(plus(x0, x1), x2, x3)) -> c9(MARK(plus(x0, x1))) MARK(plus(x0, U11(U11(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__U11(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U11(U12(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__U12(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U11(plus(z0, z1), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(tt, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U11(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U11(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(s(z0), U11(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(x0, U11(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U11(x1, x2, x3))) -> c10(A__PLUS(tt, a__U11(mark(x1), x2, x3))) MARK(plus(0, U11(x1, x2, x3))) -> c10(A__PLUS(0, a__U11(mark(x1), x2, x3))) MARK(plus(x0, U12(U11(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__U11(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U12(U12(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__U12(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U12(plus(z0, z1), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(x0)) MARK(plus(x0, U12(tt, x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U12(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U12(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U12(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U12(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U12(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(s(z0), U12(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(x0, U12(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U12(x1, x2, x3))) -> c10(A__PLUS(tt, a__U12(mark(x1), x2, x3))) MARK(plus(0, U12(x1, x2, x3))) -> c10(A__PLUS(0, a__U12(mark(x1), x2, x3))) MARK(plus(x0, plus(x1, U11(z0, z1, z2)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__U11(mark(z0), z1, z2))), MARK(x0)) MARK(plus(x0, plus(x1, U12(z0, z1, z2)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__U12(mark(z0), z1, z2))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(U11(z0, z1, z2), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__U11(mark(z0), z1, z2), mark(x2))), MARK(x0)) MARK(plus(x0, plus(U12(z0, z1, z2), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__U12(mark(z0), z1, z2), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c10(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c10(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c10(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(U11(z0, z1, z2), plus(x1, x2))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), plus(x1, x2))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c10(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))) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c10(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c10(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c10(A__PLUS(0, a__plus(mark(x1), mark(x2)))) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), 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MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) 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x1, x2))) MARK(U12(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U12(U11(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U12(U11(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U12(U11(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U12(U11(x0, z1, z2), x3, x4)) -> c9(MARK(U11(x0, z1, z2))) MARK(U12(U11(0, x1, x2), x3, x4)) -> c9(A__U12(a__U11(0, x1, x2), x3, x4)) MARK(U12(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U12(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U12(U12(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U12(U12(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U12(U12(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U12(U12(x0, z1, z2), x3, x4)) -> c9(MARK(U12(x0, z1, z2))) MARK(U12(U12(0, x1, x2), x3, x4)) -> c9(A__U12(a__U12(0, x1, x2), x3, x4)) MARK(U12(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U12(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U12(plus(x0, plus(z0, z1)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U12(plus(x0, tt), x2, x3)) -> c9(A__U12(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U12(plus(x0, s(z0)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U12(plus(x0, 0), x2, x3)) -> c9(A__U12(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U12(plus(U11(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U12(plus(U12(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U12(plus(plus(z0, z1), x1), x2, x3)) -> c9(A__U12(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U12(plus(tt, x1), x2, x3)) -> c9(A__U12(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U12(plus(s(z0), x1), x2, x3)) -> c9(A__U12(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U12(plus(0, x1), x2, x3)) -> c9(A__U12(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U12(plus(x0, x1), x2, x3)) -> c9(MARK(plus(x0, x1))) MARK(plus(x0, U11(U11(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__U11(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U11(U12(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__U12(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U11(plus(z0, z1), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(tt, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U11(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U11(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(s(z0), U11(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(x0, U11(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U11(x1, x2, x3))) -> c10(A__PLUS(tt, a__U11(mark(x1), x2, x3))) MARK(plus(0, U11(x1, x2, x3))) -> c10(A__PLUS(0, a__U11(mark(x1), x2, x3))) MARK(plus(x0, U12(U11(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__U11(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U12(U12(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__U12(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U12(plus(z0, z1), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(x0)) MARK(plus(x0, U12(tt, x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U12(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U12(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U12(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U12(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U12(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(s(z0), U12(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(x0, U12(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U12(x1, x2, x3))) -> c10(A__PLUS(tt, a__U12(mark(x1), x2, x3))) MARK(plus(0, U12(x1, x2, x3))) -> c10(A__PLUS(0, a__U12(mark(x1), x2, x3))) MARK(plus(x0, plus(x1, U11(z0, z1, z2)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__U11(mark(z0), z1, z2))), MARK(x0)) MARK(plus(x0, plus(x1, U12(z0, z1, z2)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__U12(mark(z0), z1, z2))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(U11(z0, z1, z2), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__U11(mark(z0), z1, z2), mark(x2))), MARK(x0)) MARK(plus(x0, plus(U12(z0, z1, z2), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__U12(mark(z0), z1, z2), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c10(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c10(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c10(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(U11(z0, z1, z2), plus(x1, x2))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), plus(x1, x2))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c10(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))) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c10(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c10(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c10(A__PLUS(0, a__plus(mark(x1), mark(x2)))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_1, c9_1, c10_2, c10_1, c11_2, c11_1, c8_2, c9_2 ---------------------------------------- (177) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(U11(z0, z1, z2), x1)) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) by MARK(plus(U11(x0, x1, x2), U11(z0, z1, z2))) -> c10(A__PLUS(a__U11(mark(x0), x1, x2), a__U11(mark(z0), z1, z2)), MARK(U11(x0, x1, x2))) MARK(plus(U11(x0, x1, x2), U12(z0, z1, z2))) -> c10(A__PLUS(a__U11(mark(x0), x1, x2), a__U12(mark(z0), z1, z2)), MARK(U11(x0, x1, x2))) MARK(plus(U11(x0, x1, x2), plus(z0, z1))) -> c10(A__PLUS(a__U11(mark(x0), x1, x2), a__plus(mark(z0), mark(z1))), MARK(U11(x0, x1, x2))) MARK(plus(U11(x0, x1, x2), tt)) -> c10(A__PLUS(a__U11(mark(x0), x1, x2), tt), MARK(U11(x0, x1, x2))) MARK(plus(U11(x0, x1, x2), s(z0))) -> c10(A__PLUS(a__U11(mark(x0), x1, x2), s(mark(z0))), MARK(U11(x0, x1, x2))) MARK(plus(U11(x0, x1, x2), 0)) -> c10(A__PLUS(a__U11(mark(x0), x1, x2), 0), MARK(U11(x0, x1, x2))) MARK(plus(U11(x0, z1, z2), x3)) -> c10(A__PLUS(U11(mark(x0), z1, z2), mark(x3)), MARK(U11(x0, z1, z2))) MARK(plus(U11(U11(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(plus(U11(U12(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(plus(U11(plus(z0, z1), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(U11(plus(z0, z1), x1, x2))) MARK(plus(U11(tt, x1, x2), x3)) -> c10(A__PLUS(a__U11(tt, x1, x2), mark(x3)), MARK(U11(tt, x1, x2))) MARK(plus(U11(s(z0), x1, x2), x3)) -> c10(A__PLUS(a__U11(s(mark(z0)), x1, x2), mark(x3)), MARK(U11(s(z0), x1, x2))) MARK(plus(U11(0, x1, x2), x3)) -> c10(A__PLUS(a__U11(0, x1, x2), mark(x3)), MARK(U11(0, x1, x2))) ---------------------------------------- (178) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, 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x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U12(U12(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U12(U12(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U12(U12(x0, z1, z2), x3, x4)) -> c9(MARK(U12(x0, z1, z2))) MARK(U12(U12(0, x1, x2), x3, x4)) -> c9(A__U12(a__U12(0, x1, x2), x3, x4)) MARK(U12(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U12(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U12(plus(x0, plus(z0, z1)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U12(plus(x0, tt), x2, x3)) -> c9(A__U12(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U12(plus(x0, s(z0)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U12(plus(x0, 0), x2, x3)) -> c9(A__U12(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U12(plus(U11(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U12(plus(U12(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U12(plus(plus(z0, z1), x1), x2, x3)) -> c9(A__U12(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U12(plus(tt, x1), x2, x3)) -> c9(A__U12(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U12(plus(s(z0), x1), x2, x3)) -> c9(A__U12(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U12(plus(0, x1), x2, x3)) -> c9(A__U12(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U12(plus(x0, x1), x2, x3)) -> c9(MARK(plus(x0, x1))) MARK(plus(x0, U11(U11(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__U11(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U11(U12(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__U12(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U11(plus(z0, z1), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(tt, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U11(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U11(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(s(z0), U11(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(x0, U11(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U11(x1, x2, x3))) -> c10(A__PLUS(tt, a__U11(mark(x1), x2, x3))) MARK(plus(0, U11(x1, x2, x3))) -> c10(A__PLUS(0, a__U11(mark(x1), x2, x3))) MARK(plus(x0, U12(U11(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__U11(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U12(U12(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__U12(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U12(plus(z0, z1), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(x0)) MARK(plus(x0, U12(tt, x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U12(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U12(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U12(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U12(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U12(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(s(z0), U12(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(x0, U12(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U12(x1, x2, x3))) -> c10(A__PLUS(tt, a__U12(mark(x1), x2, x3))) MARK(plus(0, U12(x1, x2, x3))) -> c10(A__PLUS(0, a__U12(mark(x1), x2, x3))) MARK(plus(x0, plus(x1, U11(z0, z1, z2)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__U11(mark(z0), z1, z2))), MARK(x0)) MARK(plus(x0, plus(x1, U12(z0, z1, z2)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__U12(mark(z0), z1, z2))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(U11(z0, z1, z2), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__U11(mark(z0), z1, z2), mark(x2))), MARK(x0)) MARK(plus(x0, plus(U12(z0, z1, z2), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__U12(mark(z0), z1, z2), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c10(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c10(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c10(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(U11(z0, z1, z2), plus(x1, x2))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), plus(x1, x2))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c10(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))) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c10(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c10(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c10(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(U11(x0, x1, x2), tt)) -> c10(A__PLUS(a__U11(mark(x0), x1, x2), tt), MARK(U11(x0, x1, x2))) MARK(plus(U11(x0, x1, x2), s(z0))) -> c10(A__PLUS(a__U11(mark(x0), x1, x2), s(mark(z0))), MARK(U11(x0, x1, x2))) MARK(plus(U11(x0, x1, x2), 0)) -> c10(A__PLUS(a__U11(mark(x0), x1, x2), 0), MARK(U11(x0, x1, x2))) MARK(plus(U11(x0, z1, z2), x3)) -> c10(A__PLUS(U11(mark(x0), z1, z2), mark(x3)), MARK(U11(x0, z1, z2))) MARK(plus(U11(U11(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(plus(U11(U12(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(plus(U11(plus(z0, z1), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(U11(plus(z0, z1), x1, x2))) MARK(plus(U11(tt, x1, x2), x3)) -> c10(A__PLUS(a__U11(tt, x1, x2), mark(x3)), MARK(U11(tt, x1, x2))) MARK(plus(U11(s(z0), x1, x2), x3)) -> c10(A__PLUS(a__U11(s(mark(z0)), x1, x2), mark(x3)), MARK(U11(s(z0), x1, x2))) MARK(plus(U11(0, x1, x2), x3)) -> c10(A__PLUS(a__U11(0, x1, x2), mark(x3)), MARK(U11(0, x1, x2))) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), 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x1))) MARK(U11(plus(s(z0), x1), x2, x3)) -> c8(A__U11(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U11(plus(0, x1), x2, x3)) -> c8(A__U11(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U11(plus(x0, x1), x2, x3)) -> c8(MARK(plus(x0, x1))) MARK(U12(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U12(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U12(U11(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U12(U11(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U12(U11(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U12(U11(x0, z1, z2), x3, x4)) -> c9(MARK(U11(x0, z1, z2))) MARK(U12(U11(0, x1, x2), x3, x4)) -> c9(A__U12(a__U11(0, x1, x2), x3, x4)) MARK(U12(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U12(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U12(U12(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U12(U12(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U12(U12(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U12(U12(x0, z1, z2), x3, x4)) -> c9(MARK(U12(x0, z1, z2))) MARK(U12(U12(0, x1, x2), x3, x4)) -> c9(A__U12(a__U12(0, x1, x2), x3, x4)) MARK(U12(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U12(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U12(plus(x0, plus(z0, z1)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U12(plus(x0, tt), x2, x3)) -> c9(A__U12(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U12(plus(x0, s(z0)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U12(plus(x0, 0), x2, x3)) -> c9(A__U12(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U12(plus(U11(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U12(plus(U12(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U12(plus(plus(z0, z1), x1), x2, x3)) -> c9(A__U12(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U12(plus(tt, x1), x2, x3)) -> c9(A__U12(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U12(plus(s(z0), x1), x2, x3)) -> c9(A__U12(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U12(plus(0, x1), x2, x3)) -> c9(A__U12(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U12(plus(x0, x1), x2, x3)) -> c9(MARK(plus(x0, x1))) MARK(plus(x0, U11(U11(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__U11(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U11(U12(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__U12(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U11(plus(z0, z1), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(tt, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U11(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U11(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(s(z0), U11(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(x0, U11(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U11(x1, x2, x3))) -> c10(A__PLUS(tt, a__U11(mark(x1), x2, x3))) MARK(plus(0, U11(x1, x2, x3))) -> c10(A__PLUS(0, a__U11(mark(x1), x2, x3))) MARK(plus(x0, U12(U11(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__U11(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U12(U12(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__U12(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U12(plus(z0, z1), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(x0)) MARK(plus(x0, U12(tt, x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U12(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U12(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U12(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U12(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U12(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(s(z0), U12(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(x0, U12(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U12(x1, x2, x3))) -> c10(A__PLUS(tt, a__U12(mark(x1), x2, x3))) MARK(plus(0, U12(x1, x2, x3))) -> c10(A__PLUS(0, a__U12(mark(x1), x2, x3))) MARK(plus(x0, plus(x1, U11(z0, z1, z2)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__U11(mark(z0), z1, z2))), MARK(x0)) MARK(plus(x0, plus(x1, U12(z0, z1, z2)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__U12(mark(z0), z1, z2))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(U11(z0, z1, z2), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__U11(mark(z0), z1, z2), mark(x2))), MARK(x0)) MARK(plus(x0, plus(U12(z0, z1, z2), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__U12(mark(z0), z1, z2), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c10(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c10(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c10(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(U11(z0, z1, z2), plus(x1, x2))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), plus(x1, x2))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c10(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))) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c10(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c10(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c10(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(U11(x0, x1, x2), tt)) -> c10(A__PLUS(a__U11(mark(x0), x1, x2), tt), MARK(U11(x0, x1, x2))) MARK(plus(U11(x0, x1, x2), s(z0))) -> c10(A__PLUS(a__U11(mark(x0), x1, x2), s(mark(z0))), MARK(U11(x0, x1, x2))) MARK(plus(U11(x0, x1, x2), 0)) -> c10(A__PLUS(a__U11(mark(x0), x1, x2), 0), MARK(U11(x0, x1, x2))) MARK(plus(U11(x0, z1, z2), x3)) -> c10(A__PLUS(U11(mark(x0), z1, z2), mark(x3)), MARK(U11(x0, z1, z2))) MARK(plus(U11(U11(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(plus(U11(U12(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(plus(U11(plus(z0, z1), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(U11(plus(z0, z1), x1, x2))) MARK(plus(U11(tt, x1, x2), x3)) -> c10(A__PLUS(a__U11(tt, x1, x2), mark(x3)), MARK(U11(tt, x1, x2))) MARK(plus(U11(s(z0), x1, x2), x3)) -> c10(A__PLUS(a__U11(s(mark(z0)), x1, x2), mark(x3)), MARK(U11(s(z0), x1, x2))) MARK(plus(U11(0, x1, x2), x3)) -> c10(A__PLUS(a__U11(0, x1, x2), mark(x3)), MARK(U11(0, x1, x2))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_1, c9_1, c10_2, c10_1, c11_2, c11_1, c8_2, c9_2 ---------------------------------------- (179) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (180) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, 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U12(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U12(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(s(z0), U12(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(x0, U12(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U12(x1, x2, x3))) -> c10(A__PLUS(tt, a__U12(mark(x1), x2, x3))) MARK(plus(0, U12(x1, x2, x3))) -> c10(A__PLUS(0, a__U12(mark(x1), x2, x3))) MARK(plus(x0, plus(x1, U11(z0, z1, z2)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__U11(mark(z0), z1, z2))), MARK(x0)) MARK(plus(x0, plus(x1, U12(z0, z1, z2)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__U12(mark(z0), z1, z2))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(U11(z0, z1, z2), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__U11(mark(z0), z1, z2), mark(x2))), MARK(x0)) MARK(plus(x0, plus(U12(z0, z1, z2), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__U12(mark(z0), z1, z2), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c10(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c10(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c10(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(U11(z0, z1, z2), plus(x1, x2))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), plus(x1, x2))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c10(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))) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c10(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c10(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c10(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(U11(x0, x1, x2), s(z0))) -> c10(A__PLUS(a__U11(mark(x0), x1, x2), s(mark(z0))), MARK(U11(x0, x1, x2))) MARK(plus(U11(x0, x1, x2), 0)) -> c10(A__PLUS(a__U11(mark(x0), x1, x2), 0), MARK(U11(x0, x1, x2))) MARK(plus(U11(x0, z1, z2), x3)) -> c10(A__PLUS(U11(mark(x0), z1, z2), mark(x3)), MARK(U11(x0, z1, z2))) MARK(plus(U11(U11(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(plus(U11(U12(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(plus(U11(plus(z0, z1), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(U11(plus(z0, z1), x1, x2))) MARK(plus(U11(tt, x1, x2), x3)) -> c10(A__PLUS(a__U11(tt, x1, x2), mark(x3)), MARK(U11(tt, x1, x2))) MARK(plus(U11(s(z0), x1, x2), x3)) -> c10(A__PLUS(a__U11(s(mark(z0)), x1, x2), mark(x3)), MARK(U11(s(z0), x1, x2))) MARK(plus(U11(x0, x1, x2), tt)) -> c10(MARK(U11(x0, x1, x2))) MARK(plus(U11(0, x1, x2), x3)) -> c10(A__PLUS(a__U11(0, x1, x2), mark(x3))) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, 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plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), 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MARK(plus(0, x1))) MARK(U11(plus(x0, x1), x2, x3)) -> c8(MARK(plus(x0, x1))) MARK(U12(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U12(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U12(U11(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U12(U11(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U12(U11(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U12(U11(x0, z1, z2), x3, x4)) -> c9(MARK(U11(x0, z1, z2))) MARK(U12(U11(0, x1, x2), x3, x4)) -> c9(A__U12(a__U11(0, x1, x2), x3, x4)) MARK(U12(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U12(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U12(U12(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U12(U12(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U12(U12(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U12(U12(x0, z1, z2), x3, x4)) -> c9(MARK(U12(x0, z1, z2))) MARK(U12(U12(0, x1, x2), x3, x4)) -> c9(A__U12(a__U12(0, x1, x2), x3, x4)) MARK(U12(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U12(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U12(plus(x0, plus(z0, z1)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U12(plus(x0, tt), x2, x3)) -> c9(A__U12(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U12(plus(x0, s(z0)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U12(plus(x0, 0), x2, x3)) -> c9(A__U12(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U12(plus(U11(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U12(plus(U12(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U12(plus(plus(z0, z1), x1), x2, x3)) -> c9(A__U12(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U12(plus(tt, x1), x2, x3)) -> c9(A__U12(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U12(plus(s(z0), x1), x2, x3)) -> c9(A__U12(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U12(plus(0, x1), x2, x3)) -> c9(A__U12(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U12(plus(x0, x1), x2, x3)) -> c9(MARK(plus(x0, x1))) MARK(plus(x0, U11(U11(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__U11(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U11(U12(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__U12(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U11(plus(z0, z1), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(tt, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U11(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U11(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(s(z0), U11(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(x0, U11(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U11(x1, x2, x3))) -> c10(A__PLUS(tt, a__U11(mark(x1), x2, x3))) MARK(plus(0, U11(x1, x2, x3))) -> c10(A__PLUS(0, a__U11(mark(x1), x2, x3))) MARK(plus(x0, U12(U11(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__U11(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U12(U12(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__U12(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U12(plus(z0, z1), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(x0)) MARK(plus(x0, U12(tt, x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U12(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U12(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U12(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U12(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U12(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(s(z0), U12(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(x0, U12(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U12(x1, x2, x3))) -> c10(A__PLUS(tt, a__U12(mark(x1), x2, x3))) MARK(plus(0, U12(x1, x2, x3))) -> c10(A__PLUS(0, a__U12(mark(x1), x2, x3))) MARK(plus(x0, plus(x1, U11(z0, z1, z2)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__U11(mark(z0), z1, z2))), MARK(x0)) MARK(plus(x0, plus(x1, U12(z0, z1, z2)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__U12(mark(z0), z1, z2))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(U11(z0, z1, z2), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__U11(mark(z0), z1, z2), mark(x2))), MARK(x0)) MARK(plus(x0, plus(U12(z0, z1, z2), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__U12(mark(z0), z1, z2), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c10(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c10(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c10(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(U11(z0, z1, z2), plus(x1, x2))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), plus(x1, x2))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c10(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))) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c10(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c10(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c10(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(U11(x0, x1, x2), s(z0))) -> c10(A__PLUS(a__U11(mark(x0), x1, x2), s(mark(z0))), MARK(U11(x0, x1, x2))) MARK(plus(U11(x0, x1, x2), 0)) -> c10(A__PLUS(a__U11(mark(x0), x1, x2), 0), MARK(U11(x0, x1, x2))) MARK(plus(U11(x0, z1, z2), x3)) -> c10(A__PLUS(U11(mark(x0), z1, z2), mark(x3)), MARK(U11(x0, z1, z2))) MARK(plus(U11(U11(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(plus(U11(U12(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(plus(U11(plus(z0, z1), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(U11(plus(z0, z1), x1, x2))) MARK(plus(U11(tt, x1, x2), x3)) -> c10(A__PLUS(a__U11(tt, x1, x2), mark(x3)), MARK(U11(tt, x1, x2))) MARK(plus(U11(s(z0), x1, x2), x3)) -> c10(A__PLUS(a__U11(s(mark(z0)), x1, x2), mark(x3)), MARK(U11(s(z0), x1, x2))) MARK(plus(U11(x0, x1, x2), tt)) -> c10(MARK(U11(x0, x1, x2))) MARK(plus(U11(0, x1, x2), x3)) -> c10(A__PLUS(a__U11(0, x1, x2), mark(x3))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_1, c9_1, c10_2, c10_1, c11_2, c11_1, c8_2, c9_2 ---------------------------------------- (181) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(U12(z0, z1, z2), x1)) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) by MARK(plus(U12(x0, x1, x2), U11(z0, z1, z2))) -> c10(A__PLUS(a__U12(mark(x0), x1, x2), a__U11(mark(z0), z1, z2)), MARK(U12(x0, x1, x2))) MARK(plus(U12(x0, x1, x2), U12(z0, z1, z2))) -> c10(A__PLUS(a__U12(mark(x0), x1, x2), a__U12(mark(z0), z1, z2)), MARK(U12(x0, x1, x2))) MARK(plus(U12(x0, x1, x2), plus(z0, z1))) -> c10(A__PLUS(a__U12(mark(x0), x1, x2), a__plus(mark(z0), mark(z1))), MARK(U12(x0, x1, x2))) MARK(plus(U12(x0, x1, x2), tt)) -> c10(A__PLUS(a__U12(mark(x0), x1, x2), tt), MARK(U12(x0, x1, x2))) MARK(plus(U12(x0, x1, x2), s(z0))) -> c10(A__PLUS(a__U12(mark(x0), x1, x2), s(mark(z0))), MARK(U12(x0, x1, x2))) MARK(plus(U12(x0, x1, x2), 0)) -> c10(A__PLUS(a__U12(mark(x0), x1, x2), 0), MARK(U12(x0, x1, x2))) MARK(plus(U12(x0, z1, z2), x3)) -> c10(A__PLUS(U12(mark(x0), z1, z2), mark(x3)), MARK(U12(x0, z1, z2))) MARK(plus(U12(U11(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(plus(U12(U12(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(plus(U12(plus(z0, z1), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(U12(plus(z0, z1), x1, x2))) MARK(plus(U12(tt, x1, x2), x3)) -> c10(A__PLUS(a__U12(tt, x1, x2), mark(x3)), MARK(U12(tt, x1, x2))) MARK(plus(U12(s(z0), x1, x2), x3)) -> c10(A__PLUS(a__U12(s(mark(z0)), x1, x2), mark(x3)), MARK(U12(s(z0), x1, x2))) MARK(plus(U12(0, x1, x2), x3)) -> c10(A__PLUS(a__U12(0, x1, x2), mark(x3)), MARK(U12(0, x1, x2))) ---------------------------------------- (182) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), 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c10(A__PLUS(a__U12(s(mark(z0)), x1, x2), mark(x3)), MARK(U12(s(z0), x1, x2))) MARK(plus(U12(0, x1, x2), x3)) -> c10(A__PLUS(a__U12(0, x1, x2), mark(x3)), MARK(U12(0, x1, x2))) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U12(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c3(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c3(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U12(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U12(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U12(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, 0) -> c3(A__PLUS(0, 0)) MARK(U11(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U11(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U11(U11(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U11(U11(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U11(U11(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U11(U11(x0, z1, z2), x3, x4)) -> c8(MARK(U11(x0, z1, z2))) MARK(U11(U11(0, x1, x2), x3, x4)) -> c8(A__U11(a__U11(0, x1, x2), x3, x4)) MARK(U11(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U11(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U11(U12(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U11(U12(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U11(U12(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U11(U12(x0, z1, z2), x3, x4)) -> c8(MARK(U12(x0, z1, z2))) MARK(U11(U12(0, x1, x2), x3, x4)) -> c8(A__U11(a__U12(0, x1, x2), x3, x4)) MARK(U11(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U11(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U11(plus(x0, plus(z0, z1)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U11(plus(x0, tt), x2, x3)) -> c8(A__U11(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U11(plus(x0, s(z0)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U11(plus(x0, 0), x2, x3)) -> c8(A__U11(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U11(plus(U11(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U11(plus(U12(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U11(plus(plus(z0, z1), x1), x2, x3)) -> c8(A__U11(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U11(plus(tt, x1), x2, x3)) -> c8(A__U11(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U11(plus(s(z0), x1), x2, x3)) -> c8(A__U11(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U11(plus(0, x1), x2, x3)) -> c8(A__U11(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U11(plus(x0, x1), x2, x3)) -> c8(MARK(plus(x0, x1))) MARK(U12(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U12(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U12(U11(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U12(U11(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U12(U11(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U12(U11(x0, z1, z2), x3, x4)) -> c9(MARK(U11(x0, z1, z2))) MARK(U12(U11(0, x1, x2), x3, x4)) -> c9(A__U12(a__U11(0, x1, x2), x3, x4)) MARK(U12(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U12(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U12(U12(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U12(U12(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U12(U12(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U12(U12(x0, z1, z2), x3, x4)) -> c9(MARK(U12(x0, z1, z2))) MARK(U12(U12(0, x1, x2), x3, x4)) -> c9(A__U12(a__U12(0, x1, x2), x3, x4)) MARK(U12(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U12(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U12(plus(x0, plus(z0, z1)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U12(plus(x0, tt), x2, x3)) -> c9(A__U12(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U12(plus(x0, s(z0)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U12(plus(x0, 0), x2, x3)) -> c9(A__U12(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U12(plus(U11(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U12(plus(U12(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U12(plus(plus(z0, z1), x1), x2, x3)) -> c9(A__U12(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U12(plus(tt, x1), x2, x3)) -> c9(A__U12(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U12(plus(s(z0), x1), x2, x3)) -> c9(A__U12(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U12(plus(0, x1), x2, x3)) -> c9(A__U12(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U12(plus(x0, x1), x2, x3)) -> c9(MARK(plus(x0, x1))) MARK(plus(x0, U11(U11(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__U11(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U11(U12(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__U12(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U11(plus(z0, z1), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(tt, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U11(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U11(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(s(z0), U11(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(x0, U11(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U11(x1, x2, x3))) -> c10(A__PLUS(tt, a__U11(mark(x1), x2, x3))) MARK(plus(0, U11(x1, x2, x3))) -> c10(A__PLUS(0, a__U11(mark(x1), x2, x3))) MARK(plus(x0, U12(U11(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__U11(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U12(U12(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__U12(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U12(plus(z0, z1), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(x0)) MARK(plus(x0, U12(tt, x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U12(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U12(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U12(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U12(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U12(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(s(z0), U12(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(x0, U12(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U12(x1, x2, x3))) -> c10(A__PLUS(tt, a__U12(mark(x1), x2, x3))) MARK(plus(0, U12(x1, x2, x3))) -> c10(A__PLUS(0, a__U12(mark(x1), x2, x3))) MARK(plus(x0, plus(x1, U11(z0, z1, z2)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__U11(mark(z0), z1, z2))), MARK(x0)) MARK(plus(x0, plus(x1, U12(z0, z1, z2)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__U12(mark(z0), z1, z2))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(U11(z0, z1, z2), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__U11(mark(z0), z1, z2), mark(x2))), MARK(x0)) MARK(plus(x0, plus(U12(z0, z1, z2), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__U12(mark(z0), z1, z2), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c10(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c10(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c10(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(U11(z0, z1, z2), plus(x1, x2))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), plus(x1, x2))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c10(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))) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c10(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c10(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c10(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(U11(x0, x1, x2), s(z0))) -> c10(A__PLUS(a__U11(mark(x0), x1, x2), s(mark(z0))), MARK(U11(x0, x1, x2))) MARK(plus(U11(x0, x1, x2), 0)) -> c10(A__PLUS(a__U11(mark(x0), x1, x2), 0), MARK(U11(x0, x1, x2))) MARK(plus(U11(x0, z1, z2), x3)) -> c10(A__PLUS(U11(mark(x0), z1, z2), mark(x3)), MARK(U11(x0, z1, z2))) MARK(plus(U11(U11(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(plus(U11(U12(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(plus(U11(plus(z0, z1), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(U11(plus(z0, z1), x1, x2))) MARK(plus(U11(tt, x1, x2), x3)) -> c10(A__PLUS(a__U11(tt, x1, x2), mark(x3)), MARK(U11(tt, x1, x2))) MARK(plus(U11(s(z0), x1, x2), x3)) -> c10(A__PLUS(a__U11(s(mark(z0)), x1, x2), mark(x3)), MARK(U11(s(z0), x1, x2))) MARK(plus(U11(x0, x1, x2), tt)) -> c10(MARK(U11(x0, x1, x2))) MARK(plus(U11(0, x1, x2), x3)) -> c10(A__PLUS(a__U11(0, x1, x2), mark(x3))) MARK(plus(U12(x0, x1, x2), tt)) -> c10(A__PLUS(a__U12(mark(x0), x1, x2), tt), MARK(U12(x0, x1, x2))) MARK(plus(U12(x0, x1, x2), s(z0))) -> c10(A__PLUS(a__U12(mark(x0), x1, x2), s(mark(z0))), MARK(U12(x0, x1, x2))) MARK(plus(U12(x0, x1, x2), 0)) -> c10(A__PLUS(a__U12(mark(x0), x1, x2), 0), MARK(U12(x0, x1, x2))) MARK(plus(U12(x0, z1, z2), x3)) -> c10(A__PLUS(U12(mark(x0), z1, z2), mark(x3)), MARK(U12(x0, z1, z2))) MARK(plus(U12(U11(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(plus(U12(U12(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(plus(U12(plus(z0, z1), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(U12(plus(z0, z1), x1, x2))) MARK(plus(U12(tt, x1, x2), x3)) -> c10(A__PLUS(a__U12(tt, x1, x2), mark(x3)), MARK(U12(tt, x1, x2))) MARK(plus(U12(s(z0), x1, x2), x3)) -> c10(A__PLUS(a__U12(s(mark(z0)), x1, x2), mark(x3)), MARK(U12(s(z0), x1, x2))) MARK(plus(U12(0, x1, x2), x3)) -> c10(A__PLUS(a__U12(0, x1, x2), mark(x3)), MARK(U12(0, x1, x2))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_1, c9_1, c10_2, c10_1, c11_2, c11_1, c8_2, c9_2 ---------------------------------------- (183) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (184) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> 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x2), s(mark(z0))), MARK(U12(x0, x1, x2))) MARK(plus(U12(x0, x1, x2), 0)) -> c10(A__PLUS(a__U12(mark(x0), x1, x2), 0), MARK(U12(x0, x1, x2))) MARK(plus(U12(x0, z1, z2), x3)) -> c10(A__PLUS(U12(mark(x0), z1, z2), mark(x3)), MARK(U12(x0, z1, z2))) MARK(plus(U12(U11(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(plus(U12(U12(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(plus(U12(plus(z0, z1), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(U12(plus(z0, z1), x1, x2))) MARK(plus(U12(tt, x1, x2), x3)) -> c10(A__PLUS(a__U12(tt, x1, x2), mark(x3)), MARK(U12(tt, x1, x2))) MARK(plus(U12(s(z0), x1, x2), x3)) -> c10(A__PLUS(a__U12(s(mark(z0)), x1, x2), mark(x3)), MARK(U12(s(z0), x1, x2))) MARK(plus(U12(x0, x1, x2), tt)) -> c10(MARK(U12(x0, x1, x2))) MARK(plus(U12(0, x1, x2), x3)) -> c10(A__PLUS(a__U12(0, x1, x2), mark(x3))) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), 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U12(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U12(x1, x2, x3))) -> c10(A__PLUS(tt, a__U12(mark(x1), x2, x3))) MARK(plus(0, U12(x1, x2, x3))) -> c10(A__PLUS(0, a__U12(mark(x1), x2, x3))) MARK(plus(x0, plus(x1, U11(z0, z1, z2)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__U11(mark(z0), z1, z2))), MARK(x0)) MARK(plus(x0, plus(x1, U12(z0, z1, z2)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__U12(mark(z0), z1, z2))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(U11(z0, z1, z2), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__U11(mark(z0), z1, z2), mark(x2))), MARK(x0)) MARK(plus(x0, plus(U12(z0, z1, z2), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__U12(mark(z0), z1, z2), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c10(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c10(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c10(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(U11(z0, z1, z2), plus(x1, x2))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), plus(x1, x2))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c10(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))) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c10(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c10(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c10(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(U11(x0, x1, x2), s(z0))) -> c10(A__PLUS(a__U11(mark(x0), x1, x2), s(mark(z0))), MARK(U11(x0, x1, x2))) MARK(plus(U11(x0, x1, x2), 0)) -> c10(A__PLUS(a__U11(mark(x0), x1, x2), 0), MARK(U11(x0, x1, x2))) MARK(plus(U11(x0, z1, z2), x3)) -> c10(A__PLUS(U11(mark(x0), z1, z2), mark(x3)), MARK(U11(x0, z1, z2))) MARK(plus(U11(U11(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(plus(U11(U12(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(plus(U11(plus(z0, z1), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(U11(plus(z0, z1), x1, x2))) MARK(plus(U11(tt, x1, x2), x3)) -> c10(A__PLUS(a__U11(tt, x1, x2), mark(x3)), MARK(U11(tt, x1, x2))) MARK(plus(U11(s(z0), x1, x2), x3)) -> c10(A__PLUS(a__U11(s(mark(z0)), x1, x2), mark(x3)), MARK(U11(s(z0), x1, x2))) MARK(plus(U11(x0, x1, x2), tt)) -> c10(MARK(U11(x0, x1, x2))) MARK(plus(U11(0, x1, x2), x3)) -> c10(A__PLUS(a__U11(0, x1, x2), mark(x3))) MARK(plus(U12(x0, x1, x2), s(z0))) -> c10(A__PLUS(a__U12(mark(x0), x1, x2), s(mark(z0))), MARK(U12(x0, x1, x2))) MARK(plus(U12(x0, x1, x2), 0)) -> c10(A__PLUS(a__U12(mark(x0), x1, x2), 0), MARK(U12(x0, x1, x2))) MARK(plus(U12(x0, z1, z2), x3)) -> c10(A__PLUS(U12(mark(x0), z1, z2), mark(x3)), MARK(U12(x0, z1, z2))) MARK(plus(U12(U11(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(plus(U12(U12(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(plus(U12(plus(z0, z1), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(U12(plus(z0, z1), x1, x2))) MARK(plus(U12(tt, x1, x2), x3)) -> c10(A__PLUS(a__U12(tt, x1, x2), mark(x3)), MARK(U12(tt, x1, x2))) MARK(plus(U12(s(z0), x1, x2), x3)) -> c10(A__PLUS(a__U12(s(mark(z0)), x1, x2), mark(x3)), MARK(U12(s(z0), x1, x2))) MARK(plus(U12(x0, x1, x2), tt)) -> c10(MARK(U12(x0, x1, x2))) MARK(plus(U12(0, x1, x2), x3)) -> c10(A__PLUS(a__U12(0, x1, x2), mark(x3))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_1, c9_1, c10_2, c10_1, c11_2, c11_1, c8_2, c9_2 ---------------------------------------- (185) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(plus(z0, z1), x1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) by MARK(plus(plus(x0, x1), U11(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x0), mark(x1)), a__U11(mark(z0), z1, z2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), U12(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x0), mark(x1)), a__U12(mark(z0), z1, z2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), plus(z0, z1))) -> c10(A__PLUS(a__plus(mark(x0), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), tt)) -> c10(A__PLUS(a__plus(mark(x0), mark(x1)), tt), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), s(z0))) -> c10(A__PLUS(a__plus(mark(x0), mark(x1)), s(mark(z0))), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), 0)) -> c10(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c10(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, U11(z0, z1, z2)), x2)) -> c10(A__PLUS(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), mark(x2)), MARK(plus(x0, U11(z0, z1, z2)))) MARK(plus(plus(x0, U12(z0, z1, z2)), x2)) -> c10(A__PLUS(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), mark(x2)), MARK(plus(x0, U12(z0, z1, z2)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c10(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)) -> c10(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, s(z0)), x2)) -> c10(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(x0, 0), x2)) -> c10(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(U11(z0, z1, z2), x1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(plus(U11(z0, z1, z2), x1))) MARK(plus(plus(U12(z0, z1, z2), x1), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(plus(U12(z0, z1, z2), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c10(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)) -> c10(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(0, x1), x2)) -> c10(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) ---------------------------------------- (186) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 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a__U11(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U11(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(s(z0), U11(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(x0, U11(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U11(x1, x2, x3))) -> c10(A__PLUS(tt, a__U11(mark(x1), x2, x3))) MARK(plus(0, U11(x1, x2, x3))) -> c10(A__PLUS(0, a__U11(mark(x1), x2, x3))) MARK(plus(x0, U12(U11(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__U11(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U12(U12(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__U12(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U12(plus(z0, z1), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(x0)) MARK(plus(x0, U12(tt, x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U12(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U12(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U12(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U12(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U12(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(s(z0), U12(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(x0, U12(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U12(x1, x2, x3))) -> c10(A__PLUS(tt, a__U12(mark(x1), x2, x3))) MARK(plus(0, U12(x1, x2, x3))) -> c10(A__PLUS(0, a__U12(mark(x1), x2, x3))) MARK(plus(x0, plus(x1, U11(z0, z1, z2)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__U11(mark(z0), z1, z2))), MARK(x0)) MARK(plus(x0, plus(x1, U12(z0, z1, z2)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__U12(mark(z0), z1, z2))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(U11(z0, z1, z2), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__U11(mark(z0), z1, z2), mark(x2))), MARK(x0)) MARK(plus(x0, plus(U12(z0, z1, z2), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__U12(mark(z0), z1, z2), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c10(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c10(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c10(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(U11(z0, z1, z2), plus(x1, x2))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), plus(x1, x2))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c10(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))) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c10(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c10(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c10(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(U11(x0, x1, x2), s(z0))) -> c10(A__PLUS(a__U11(mark(x0), x1, x2), s(mark(z0))), MARK(U11(x0, x1, x2))) MARK(plus(U11(x0, x1, x2), 0)) -> c10(A__PLUS(a__U11(mark(x0), x1, x2), 0), MARK(U11(x0, x1, x2))) MARK(plus(U11(x0, z1, z2), x3)) -> c10(A__PLUS(U11(mark(x0), z1, z2), mark(x3)), MARK(U11(x0, z1, z2))) MARK(plus(U11(U11(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(plus(U11(U12(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(plus(U11(plus(z0, z1), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(U11(plus(z0, z1), x1, x2))) MARK(plus(U11(tt, x1, x2), x3)) -> c10(A__PLUS(a__U11(tt, x1, x2), mark(x3)), MARK(U11(tt, x1, x2))) MARK(plus(U11(s(z0), x1, x2), x3)) -> c10(A__PLUS(a__U11(s(mark(z0)), x1, x2), mark(x3)), MARK(U11(s(z0), x1, x2))) MARK(plus(U11(x0, x1, x2), tt)) -> c10(MARK(U11(x0, x1, x2))) MARK(plus(U11(0, x1, x2), x3)) -> c10(A__PLUS(a__U11(0, x1, x2), mark(x3))) MARK(plus(U12(x0, x1, x2), s(z0))) -> c10(A__PLUS(a__U12(mark(x0), x1, x2), s(mark(z0))), MARK(U12(x0, x1, x2))) MARK(plus(U12(x0, x1, x2), 0)) -> c10(A__PLUS(a__U12(mark(x0), x1, x2), 0), MARK(U12(x0, x1, x2))) MARK(plus(U12(x0, z1, z2), x3)) -> c10(A__PLUS(U12(mark(x0), z1, z2), mark(x3)), MARK(U12(x0, z1, z2))) MARK(plus(U12(U11(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(plus(U12(U12(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(plus(U12(plus(z0, z1), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(U12(plus(z0, z1), x1, x2))) MARK(plus(U12(tt, x1, x2), x3)) -> c10(A__PLUS(a__U12(tt, x1, x2), mark(x3)), MARK(U12(tt, x1, x2))) MARK(plus(U12(s(z0), x1, x2), x3)) -> c10(A__PLUS(a__U12(s(mark(z0)), x1, x2), mark(x3)), MARK(U12(s(z0), x1, x2))) MARK(plus(U12(x0, x1, x2), tt)) -> c10(MARK(U12(x0, x1, x2))) MARK(plus(U12(0, x1, x2), x3)) -> c10(A__PLUS(a__U12(0, x1, x2), mark(x3))) MARK(plus(plus(x0, x1), tt)) -> c10(A__PLUS(a__plus(mark(x0), mark(x1)), tt), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), s(z0))) -> c10(A__PLUS(a__plus(mark(x0), mark(x1)), s(mark(z0))), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), 0)) -> c10(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c10(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, U11(z0, z1, z2)), x2)) -> c10(A__PLUS(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), mark(x2)), MARK(plus(x0, U11(z0, z1, z2)))) MARK(plus(plus(x0, U12(z0, z1, z2)), x2)) -> c10(A__PLUS(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), mark(x2)), MARK(plus(x0, U12(z0, z1, z2)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c10(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)) -> c10(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, s(z0)), x2)) -> c10(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(x0, 0), x2)) -> c10(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(U11(z0, z1, z2), x1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(plus(U11(z0, z1, z2), x1))) MARK(plus(plus(U12(z0, z1, z2), x1), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(plus(U12(z0, z1, z2), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c10(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)) -> c10(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(0, x1), x2)) -> c10(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U12(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c3(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c3(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U12(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U12(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U12(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, 0) -> c3(A__PLUS(0, 0)) MARK(U11(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U11(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U11(U11(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U11(U11(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U11(U11(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U11(U11(x0, z1, z2), x3, x4)) -> c8(MARK(U11(x0, z1, z2))) MARK(U11(U11(0, x1, x2), x3, x4)) -> c8(A__U11(a__U11(0, x1, x2), x3, x4)) MARK(U11(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U11(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U11(U12(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U11(U12(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U11(U12(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U11(U12(x0, z1, z2), x3, x4)) -> c8(MARK(U12(x0, z1, z2))) MARK(U11(U12(0, x1, x2), x3, x4)) -> c8(A__U11(a__U12(0, x1, x2), x3, x4)) MARK(U11(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U11(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U11(plus(x0, plus(z0, z1)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U11(plus(x0, tt), x2, x3)) -> c8(A__U11(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U11(plus(x0, s(z0)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U11(plus(x0, 0), x2, x3)) -> c8(A__U11(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U11(plus(U11(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U11(plus(U12(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U11(plus(plus(z0, z1), x1), x2, x3)) -> c8(A__U11(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U11(plus(tt, x1), x2, x3)) -> c8(A__U11(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U11(plus(s(z0), x1), x2, x3)) -> c8(A__U11(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U11(plus(0, x1), x2, x3)) -> c8(A__U11(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U11(plus(x0, x1), x2, x3)) -> c8(MARK(plus(x0, x1))) MARK(U12(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U12(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U12(U11(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U12(U11(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U12(U11(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U12(U11(x0, z1, z2), x3, x4)) -> c9(MARK(U11(x0, z1, z2))) MARK(U12(U11(0, x1, x2), x3, x4)) -> c9(A__U12(a__U11(0, x1, x2), x3, x4)) MARK(U12(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U12(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U12(U12(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U12(U12(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U12(U12(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U12(U12(x0, z1, z2), x3, x4)) -> c9(MARK(U12(x0, z1, z2))) MARK(U12(U12(0, x1, x2), x3, x4)) -> c9(A__U12(a__U12(0, x1, x2), x3, x4)) MARK(U12(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U12(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U12(plus(x0, plus(z0, z1)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U12(plus(x0, tt), x2, x3)) -> c9(A__U12(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U12(plus(x0, s(z0)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U12(plus(x0, 0), x2, x3)) -> c9(A__U12(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U12(plus(U11(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U12(plus(U12(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U12(plus(plus(z0, z1), x1), x2, x3)) -> c9(A__U12(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U12(plus(tt, x1), x2, x3)) -> c9(A__U12(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U12(plus(s(z0), x1), x2, x3)) -> c9(A__U12(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U12(plus(0, x1), x2, x3)) -> c9(A__U12(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U12(plus(x0, x1), x2, x3)) -> c9(MARK(plus(x0, x1))) MARK(plus(x0, U11(U11(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__U11(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U11(U12(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__U12(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U11(plus(z0, z1), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(tt, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U11(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U11(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(s(z0), U11(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(x0, U11(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U11(x1, x2, x3))) -> c10(A__PLUS(tt, a__U11(mark(x1), x2, x3))) MARK(plus(0, U11(x1, x2, x3))) -> c10(A__PLUS(0, a__U11(mark(x1), x2, x3))) MARK(plus(x0, U12(U11(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__U11(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U12(U12(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__U12(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U12(plus(z0, z1), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(x0)) MARK(plus(x0, U12(tt, x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U12(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U12(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U12(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U12(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U12(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(s(z0), U12(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(x0, U12(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U12(x1, x2, x3))) -> c10(A__PLUS(tt, a__U12(mark(x1), x2, x3))) MARK(plus(0, U12(x1, x2, x3))) -> c10(A__PLUS(0, a__U12(mark(x1), x2, x3))) MARK(plus(x0, plus(x1, U11(z0, z1, z2)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__U11(mark(z0), z1, z2))), MARK(x0)) MARK(plus(x0, plus(x1, U12(z0, z1, z2)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__U12(mark(z0), z1, z2))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(U11(z0, z1, z2), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__U11(mark(z0), z1, z2), mark(x2))), MARK(x0)) MARK(plus(x0, plus(U12(z0, z1, z2), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__U12(mark(z0), z1, z2), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c10(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c10(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c10(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(U11(z0, z1, z2), plus(x1, x2))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), plus(x1, x2))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c10(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))) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c10(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c10(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c10(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(U11(x0, x1, x2), s(z0))) -> c10(A__PLUS(a__U11(mark(x0), x1, x2), s(mark(z0))), MARK(U11(x0, x1, x2))) MARK(plus(U11(x0, x1, x2), 0)) -> c10(A__PLUS(a__U11(mark(x0), x1, x2), 0), MARK(U11(x0, x1, x2))) MARK(plus(U11(x0, z1, z2), x3)) -> c10(A__PLUS(U11(mark(x0), z1, z2), mark(x3)), MARK(U11(x0, z1, z2))) MARK(plus(U11(U11(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(plus(U11(U12(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(plus(U11(plus(z0, z1), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(U11(plus(z0, z1), x1, x2))) MARK(plus(U11(tt, x1, x2), x3)) -> c10(A__PLUS(a__U11(tt, x1, x2), mark(x3)), MARK(U11(tt, x1, x2))) MARK(plus(U11(s(z0), x1, x2), x3)) -> c10(A__PLUS(a__U11(s(mark(z0)), x1, x2), mark(x3)), MARK(U11(s(z0), x1, x2))) MARK(plus(U11(x0, x1, x2), tt)) -> c10(MARK(U11(x0, x1, x2))) MARK(plus(U11(0, x1, x2), x3)) -> c10(A__PLUS(a__U11(0, x1, x2), mark(x3))) MARK(plus(U12(x0, x1, x2), s(z0))) -> c10(A__PLUS(a__U12(mark(x0), x1, x2), s(mark(z0))), MARK(U12(x0, x1, x2))) MARK(plus(U12(x0, x1, x2), 0)) -> c10(A__PLUS(a__U12(mark(x0), x1, x2), 0), MARK(U12(x0, x1, x2))) MARK(plus(U12(x0, z1, z2), x3)) -> c10(A__PLUS(U12(mark(x0), z1, z2), mark(x3)), MARK(U12(x0, z1, z2))) MARK(plus(U12(U11(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(plus(U12(U12(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(plus(U12(plus(z0, z1), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(U12(plus(z0, z1), x1, x2))) MARK(plus(U12(tt, x1, x2), x3)) -> c10(A__PLUS(a__U12(tt, x1, x2), mark(x3)), MARK(U12(tt, x1, x2))) MARK(plus(U12(s(z0), x1, x2), x3)) -> c10(A__PLUS(a__U12(s(mark(z0)), x1, x2), mark(x3)), MARK(U12(s(z0), x1, x2))) MARK(plus(U12(x0, x1, x2), tt)) -> c10(MARK(U12(x0, x1, x2))) MARK(plus(U12(0, x1, x2), x3)) -> c10(A__PLUS(a__U12(0, x1, x2), mark(x3))) MARK(plus(plus(x0, x1), tt)) -> c10(A__PLUS(a__plus(mark(x0), mark(x1)), tt), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), s(z0))) -> c10(A__PLUS(a__plus(mark(x0), mark(x1)), s(mark(z0))), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), 0)) -> c10(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c10(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, U11(z0, z1, z2)), x2)) -> c10(A__PLUS(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), mark(x2)), MARK(plus(x0, U11(z0, z1, z2)))) MARK(plus(plus(x0, U12(z0, z1, z2)), x2)) -> c10(A__PLUS(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), mark(x2)), MARK(plus(x0, U12(z0, z1, z2)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c10(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)) -> c10(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, s(z0)), x2)) -> c10(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(x0, 0), x2)) -> c10(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(U11(z0, z1, z2), x1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(plus(U11(z0, z1, z2), x1))) MARK(plus(plus(U12(z0, z1, z2), x1), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(plus(U12(z0, z1, z2), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c10(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)) -> c10(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(0, x1), x2)) -> c10(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_1, c9_1, c10_2, c10_1, c11_2, c11_1, c8_2, c9_2 ---------------------------------------- (187) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (188) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> 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x1))) MARK(plus(plus(tt, x1), x2)) -> c10(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(0, x1), x2)) -> c10(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(x0, x1), tt)) -> c10(MARK(plus(x0, x1))) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), 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c9(A__U12(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U12(U12(x0, z1, z2), x3, x4)) -> c9(MARK(U12(x0, z1, z2))) MARK(U12(U12(0, x1, x2), x3, x4)) -> c9(A__U12(a__U12(0, x1, x2), x3, x4)) MARK(U12(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U12(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U12(plus(x0, plus(z0, z1)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U12(plus(x0, tt), x2, x3)) -> c9(A__U12(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U12(plus(x0, s(z0)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U12(plus(x0, 0), x2, x3)) -> c9(A__U12(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U12(plus(U11(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U12(plus(U12(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U12(plus(plus(z0, z1), x1), x2, x3)) -> c9(A__U12(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U12(plus(tt, x1), x2, x3)) -> c9(A__U12(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U12(plus(s(z0), x1), x2, x3)) -> c9(A__U12(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U12(plus(0, x1), x2, x3)) -> c9(A__U12(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U12(plus(x0, x1), x2, x3)) -> c9(MARK(plus(x0, x1))) MARK(plus(x0, U11(U11(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__U11(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U11(U12(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__U12(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U11(plus(z0, z1), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(tt, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U11(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U11(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(s(z0), U11(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(x0, U11(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U11(x1, x2, x3))) -> c10(A__PLUS(tt, a__U11(mark(x1), x2, x3))) MARK(plus(0, U11(x1, x2, x3))) -> c10(A__PLUS(0, a__U11(mark(x1), x2, x3))) MARK(plus(x0, U12(U11(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__U11(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U12(U12(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__U12(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U12(plus(z0, z1), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(x0)) MARK(plus(x0, U12(tt, x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U12(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U12(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U12(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U12(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U12(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(s(z0), U12(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(x0, U12(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U12(x1, x2, x3))) -> c10(A__PLUS(tt, a__U12(mark(x1), x2, x3))) MARK(plus(0, U12(x1, x2, x3))) -> c10(A__PLUS(0, a__U12(mark(x1), x2, x3))) MARK(plus(x0, plus(x1, U11(z0, z1, z2)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__U11(mark(z0), z1, z2))), MARK(x0)) MARK(plus(x0, plus(x1, U12(z0, z1, z2)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__U12(mark(z0), z1, z2))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(U11(z0, z1, z2), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__U11(mark(z0), z1, z2), mark(x2))), MARK(x0)) MARK(plus(x0, plus(U12(z0, z1, z2), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__U12(mark(z0), z1, z2), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c10(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c10(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c10(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(U11(z0, z1, z2), plus(x1, x2))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), plus(x1, x2))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), 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-> c10(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(plus(U11(plus(z0, z1), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(U11(plus(z0, z1), x1, x2))) MARK(plus(U11(tt, x1, x2), x3)) -> c10(A__PLUS(a__U11(tt, x1, x2), mark(x3)), MARK(U11(tt, x1, x2))) MARK(plus(U11(s(z0), x1, x2), x3)) -> c10(A__PLUS(a__U11(s(mark(z0)), x1, x2), mark(x3)), MARK(U11(s(z0), x1, x2))) MARK(plus(U11(x0, x1, x2), tt)) -> c10(MARK(U11(x0, x1, x2))) MARK(plus(U11(0, x1, x2), x3)) -> c10(A__PLUS(a__U11(0, x1, x2), mark(x3))) MARK(plus(U12(x0, x1, x2), s(z0))) -> c10(A__PLUS(a__U12(mark(x0), x1, x2), s(mark(z0))), MARK(U12(x0, x1, x2))) MARK(plus(U12(x0, x1, x2), 0)) -> c10(A__PLUS(a__U12(mark(x0), x1, x2), 0), MARK(U12(x0, x1, x2))) MARK(plus(U12(x0, z1, z2), x3)) -> c10(A__PLUS(U12(mark(x0), z1, z2), mark(x3)), MARK(U12(x0, z1, z2))) MARK(plus(U12(U11(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(plus(U12(U12(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(plus(U12(plus(z0, z1), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(U12(plus(z0, z1), x1, x2))) MARK(plus(U12(tt, x1, x2), x3)) -> c10(A__PLUS(a__U12(tt, x1, x2), mark(x3)), MARK(U12(tt, x1, x2))) MARK(plus(U12(s(z0), x1, x2), x3)) -> c10(A__PLUS(a__U12(s(mark(z0)), x1, x2), mark(x3)), MARK(U12(s(z0), x1, x2))) MARK(plus(U12(x0, x1, x2), tt)) -> c10(MARK(U12(x0, x1, x2))) MARK(plus(U12(0, x1, x2), x3)) -> c10(A__PLUS(a__U12(0, x1, x2), mark(x3))) MARK(plus(plus(x0, x1), s(z0))) -> c10(A__PLUS(a__plus(mark(x0), mark(x1)), s(mark(z0))), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), 0)) -> c10(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c10(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, U11(z0, z1, z2)), x2)) -> c10(A__PLUS(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), mark(x2)), MARK(plus(x0, U11(z0, z1, z2)))) MARK(plus(plus(x0, U12(z0, z1, z2)), x2)) -> c10(A__PLUS(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), mark(x2)), MARK(plus(x0, U12(z0, z1, z2)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c10(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)) -> c10(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, s(z0)), x2)) -> c10(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(x0, 0), x2)) -> c10(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(U11(z0, z1, z2), x1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(plus(U11(z0, z1, z2), x1))) MARK(plus(plus(U12(z0, z1, z2), x1), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(plus(U12(z0, z1, z2), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c10(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)) -> c10(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(0, x1), x2)) -> c10(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(x0, x1), tt)) -> c10(MARK(plus(x0, x1))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_1, c9_1, c10_2, c10_1, c11_2, c11_1, c8_2, c9_2 ---------------------------------------- (189) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(s(z0), x1)) -> c10(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) by MARK(plus(s(x0), U11(z0, z1, z2))) -> c10(A__PLUS(s(mark(x0)), a__U11(mark(z0), z1, z2)), MARK(s(x0))) MARK(plus(s(x0), U12(z0, z1, z2))) -> c10(A__PLUS(s(mark(x0)), a__U12(mark(z0), z1, z2)), MARK(s(x0))) MARK(plus(s(x0), plus(z0, z1))) -> c10(A__PLUS(s(mark(x0)), a__plus(mark(z0), mark(z1))), MARK(s(x0))) MARK(plus(s(x0), tt)) -> c10(A__PLUS(s(mark(x0)), tt), MARK(s(x0))) MARK(plus(s(x0), s(z0))) -> c10(A__PLUS(s(mark(x0)), s(mark(z0))), MARK(s(x0))) MARK(plus(s(x0), 0)) -> c10(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(U11(z0, z1, z2)), x1)) -> c10(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x1)), MARK(s(U11(z0, z1, z2)))) MARK(plus(s(U12(z0, z1, z2)), x1)) -> c10(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x1)), MARK(s(U12(z0, z1, z2)))) MARK(plus(s(plus(z0, z1)), x1)) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c10(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(s(z0)), x1)) -> c10(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(0), x1)) -> c10(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(x0), x1)) -> c10(MARK(s(x0))) ---------------------------------------- (190) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), 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c10(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(U11(z0, z1, z2), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__U11(mark(z0), z1, z2), mark(x2))), MARK(x0)) MARK(plus(x0, plus(U12(z0, z1, z2), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__U12(mark(z0), z1, z2), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c10(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c10(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c10(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(U11(z0, z1, z2), plus(x1, x2))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), plus(x1, x2))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c10(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))) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c10(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c10(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c10(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(U11(x0, x1, x2), s(z0))) -> c10(A__PLUS(a__U11(mark(x0), x1, x2), s(mark(z0))), MARK(U11(x0, x1, x2))) MARK(plus(U11(x0, x1, x2), 0)) -> c10(A__PLUS(a__U11(mark(x0), x1, x2), 0), MARK(U11(x0, x1, x2))) MARK(plus(U11(x0, z1, z2), x3)) -> c10(A__PLUS(U11(mark(x0), z1, z2), mark(x3)), MARK(U11(x0, z1, z2))) MARK(plus(U11(U11(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(plus(U11(U12(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(plus(U11(plus(z0, z1), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(U11(plus(z0, z1), x1, x2))) MARK(plus(U11(tt, x1, x2), x3)) -> c10(A__PLUS(a__U11(tt, x1, x2), mark(x3)), MARK(U11(tt, x1, x2))) MARK(plus(U11(s(z0), x1, x2), x3)) -> c10(A__PLUS(a__U11(s(mark(z0)), x1, x2), mark(x3)), MARK(U11(s(z0), x1, x2))) MARK(plus(U11(x0, x1, x2), tt)) -> c10(MARK(U11(x0, x1, x2))) MARK(plus(U11(0, x1, x2), x3)) -> c10(A__PLUS(a__U11(0, x1, x2), mark(x3))) MARK(plus(U12(x0, x1, x2), s(z0))) -> c10(A__PLUS(a__U12(mark(x0), x1, x2), s(mark(z0))), MARK(U12(x0, x1, x2))) MARK(plus(U12(x0, x1, x2), 0)) -> c10(A__PLUS(a__U12(mark(x0), x1, x2), 0), MARK(U12(x0, x1, x2))) MARK(plus(U12(x0, z1, z2), x3)) -> c10(A__PLUS(U12(mark(x0), z1, z2), mark(x3)), MARK(U12(x0, z1, z2))) MARK(plus(U12(U11(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(plus(U12(U12(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(plus(U12(plus(z0, z1), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(U12(plus(z0, z1), x1, x2))) MARK(plus(U12(tt, x1, x2), x3)) -> c10(A__PLUS(a__U12(tt, x1, x2), mark(x3)), MARK(U12(tt, x1, x2))) MARK(plus(U12(s(z0), x1, x2), x3)) -> c10(A__PLUS(a__U12(s(mark(z0)), x1, x2), mark(x3)), MARK(U12(s(z0), x1, x2))) MARK(plus(U12(x0, x1, x2), tt)) -> c10(MARK(U12(x0, x1, x2))) MARK(plus(U12(0, x1, x2), x3)) -> c10(A__PLUS(a__U12(0, x1, x2), mark(x3))) MARK(plus(plus(x0, x1), s(z0))) -> c10(A__PLUS(a__plus(mark(x0), mark(x1)), s(mark(z0))), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), 0)) -> c10(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c10(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, U11(z0, z1, z2)), x2)) -> c10(A__PLUS(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), mark(x2)), MARK(plus(x0, U11(z0, z1, z2)))) MARK(plus(plus(x0, U12(z0, z1, z2)), x2)) -> c10(A__PLUS(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), mark(x2)), MARK(plus(x0, U12(z0, z1, z2)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c10(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)) -> c10(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, s(z0)), x2)) -> c10(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(x0, 0), x2)) -> c10(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(U11(z0, z1, z2), x1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(plus(U11(z0, z1, z2), x1))) MARK(plus(plus(U12(z0, z1, z2), x1), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(plus(U12(z0, z1, z2), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c10(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)) -> c10(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(0, x1), x2)) -> c10(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(x0, x1), tt)) -> c10(MARK(plus(x0, x1))) MARK(plus(s(x0), tt)) -> c10(A__PLUS(s(mark(x0)), tt), MARK(s(x0))) MARK(plus(s(x0), s(z0))) -> c10(A__PLUS(s(mark(x0)), s(mark(z0))), MARK(s(x0))) MARK(plus(s(x0), 0)) -> c10(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(U11(z0, z1, z2)), x1)) -> c10(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x1)), MARK(s(U11(z0, z1, z2)))) MARK(plus(s(U12(z0, z1, z2)), x1)) -> c10(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x1)), MARK(s(U12(z0, z1, z2)))) MARK(plus(s(plus(z0, z1)), x1)) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c10(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(s(z0)), x1)) -> c10(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(0), x1)) -> c10(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(x0), x1)) -> c10(MARK(s(x0))) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), 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x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U12(U12(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U12(U12(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U12(U12(x0, z1, z2), x3, x4)) -> c9(MARK(U12(x0, z1, z2))) MARK(U12(U12(0, x1, x2), x3, x4)) -> c9(A__U12(a__U12(0, x1, x2), x3, x4)) MARK(U12(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U12(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U12(plus(x0, plus(z0, z1)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U12(plus(x0, tt), x2, x3)) -> c9(A__U12(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U12(plus(x0, s(z0)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U12(plus(x0, 0), x2, x3)) -> c9(A__U12(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U12(plus(U11(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U12(plus(U12(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U12(plus(plus(z0, z1), x1), x2, x3)) -> c9(A__U12(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U12(plus(tt, x1), x2, x3)) -> c9(A__U12(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U12(plus(s(z0), x1), x2, x3)) -> c9(A__U12(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U12(plus(0, x1), x2, x3)) -> c9(A__U12(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U12(plus(x0, x1), x2, x3)) -> c9(MARK(plus(x0, x1))) MARK(plus(x0, U11(U11(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__U11(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U11(U12(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__U12(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U11(plus(z0, z1), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(tt, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U11(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U11(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(s(z0), U11(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(x0, U11(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U11(x1, x2, x3))) -> c10(A__PLUS(tt, a__U11(mark(x1), x2, x3))) MARK(plus(0, U11(x1, x2, x3))) -> c10(A__PLUS(0, a__U11(mark(x1), x2, x3))) MARK(plus(x0, U12(U11(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__U11(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U12(U12(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__U12(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U12(plus(z0, z1), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(x0)) MARK(plus(x0, U12(tt, x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U12(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U12(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U12(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U12(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U12(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(s(z0), U12(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(x0, U12(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U12(x1, x2, x3))) -> c10(A__PLUS(tt, a__U12(mark(x1), x2, x3))) MARK(plus(0, U12(x1, x2, x3))) -> c10(A__PLUS(0, a__U12(mark(x1), x2, x3))) MARK(plus(x0, plus(x1, U11(z0, z1, z2)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__U11(mark(z0), z1, z2))), MARK(x0)) MARK(plus(x0, plus(x1, U12(z0, z1, z2)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__U12(mark(z0), z1, z2))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(U11(z0, z1, z2), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__U11(mark(z0), z1, z2), mark(x2))), MARK(x0)) MARK(plus(x0, plus(U12(z0, z1, z2), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__U12(mark(z0), z1, z2), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c10(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c10(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c10(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(U11(z0, z1, z2), plus(x1, x2))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), plus(x1, x2))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c10(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))) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c10(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c10(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c10(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(U11(x0, x1, x2), s(z0))) -> c10(A__PLUS(a__U11(mark(x0), x1, x2), s(mark(z0))), MARK(U11(x0, x1, x2))) MARK(plus(U11(x0, x1, x2), 0)) -> c10(A__PLUS(a__U11(mark(x0), x1, x2), 0), MARK(U11(x0, x1, x2))) MARK(plus(U11(x0, z1, z2), x3)) -> c10(A__PLUS(U11(mark(x0), z1, z2), mark(x3)), MARK(U11(x0, z1, z2))) MARK(plus(U11(U11(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(plus(U11(U12(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(plus(U11(plus(z0, z1), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(U11(plus(z0, z1), x1, x2))) MARK(plus(U11(tt, x1, x2), x3)) -> c10(A__PLUS(a__U11(tt, x1, x2), mark(x3)), MARK(U11(tt, x1, x2))) MARK(plus(U11(s(z0), x1, x2), x3)) -> c10(A__PLUS(a__U11(s(mark(z0)), x1, x2), mark(x3)), MARK(U11(s(z0), x1, x2))) MARK(plus(U11(x0, x1, x2), tt)) -> c10(MARK(U11(x0, x1, x2))) MARK(plus(U11(0, x1, x2), x3)) -> c10(A__PLUS(a__U11(0, x1, x2), mark(x3))) MARK(plus(U12(x0, x1, x2), s(z0))) -> c10(A__PLUS(a__U12(mark(x0), x1, x2), s(mark(z0))), MARK(U12(x0, x1, x2))) MARK(plus(U12(x0, x1, x2), 0)) -> c10(A__PLUS(a__U12(mark(x0), x1, x2), 0), MARK(U12(x0, x1, x2))) MARK(plus(U12(x0, z1, z2), x3)) -> c10(A__PLUS(U12(mark(x0), z1, z2), mark(x3)), MARK(U12(x0, z1, z2))) MARK(plus(U12(U11(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(plus(U12(U12(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(plus(U12(plus(z0, z1), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(U12(plus(z0, z1), x1, x2))) MARK(plus(U12(tt, x1, x2), x3)) -> c10(A__PLUS(a__U12(tt, x1, x2), mark(x3)), MARK(U12(tt, x1, x2))) MARK(plus(U12(s(z0), x1, x2), x3)) -> c10(A__PLUS(a__U12(s(mark(z0)), x1, x2), mark(x3)), MARK(U12(s(z0), x1, x2))) MARK(plus(U12(x0, x1, x2), tt)) -> c10(MARK(U12(x0, x1, x2))) MARK(plus(U12(0, x1, x2), x3)) -> c10(A__PLUS(a__U12(0, x1, x2), mark(x3))) MARK(plus(plus(x0, x1), s(z0))) -> c10(A__PLUS(a__plus(mark(x0), mark(x1)), s(mark(z0))), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), 0)) -> c10(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c10(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, U11(z0, z1, z2)), x2)) -> c10(A__PLUS(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), mark(x2)), MARK(plus(x0, U11(z0, z1, z2)))) MARK(plus(plus(x0, U12(z0, z1, z2)), x2)) -> c10(A__PLUS(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), mark(x2)), MARK(plus(x0, U12(z0, z1, z2)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c10(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)) -> c10(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, s(z0)), x2)) -> c10(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(x0, 0), x2)) -> c10(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(U11(z0, z1, z2), x1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(plus(U11(z0, z1, z2), x1))) MARK(plus(plus(U12(z0, z1, z2), x1), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(plus(U12(z0, z1, z2), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c10(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)) -> c10(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(0, x1), x2)) -> c10(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(x0, x1), tt)) -> c10(MARK(plus(x0, x1))) MARK(plus(s(x0), tt)) -> c10(A__PLUS(s(mark(x0)), tt), MARK(s(x0))) MARK(plus(s(x0), s(z0))) -> c10(A__PLUS(s(mark(x0)), s(mark(z0))), MARK(s(x0))) MARK(plus(s(x0), 0)) -> c10(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(U11(z0, z1, z2)), x1)) -> c10(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x1)), MARK(s(U11(z0, z1, z2)))) MARK(plus(s(U12(z0, z1, z2)), x1)) -> c10(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x1)), MARK(s(U12(z0, z1, z2)))) MARK(plus(s(plus(z0, z1)), x1)) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c10(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(s(z0)), x1)) -> c10(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(0), x1)) -> c10(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(x0), x1)) -> c10(MARK(s(x0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_1, c9_1, c10_2, c10_1, c11_2, c11_1, c8_2, c9_2 ---------------------------------------- (191) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (192) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), 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MARK(plus(plus(U12(z0, z1, z2), x1), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(plus(U12(z0, z1, z2), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c10(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)) -> c10(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(0, x1), x2)) -> c10(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(x0, x1), tt)) -> c10(MARK(plus(x0, x1))) MARK(plus(s(x0), s(z0))) -> c10(A__PLUS(s(mark(x0)), s(mark(z0))), MARK(s(x0))) MARK(plus(s(x0), 0)) -> c10(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(U11(z0, z1, z2)), x1)) -> c10(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x1)), MARK(s(U11(z0, z1, z2)))) MARK(plus(s(U12(z0, z1, z2)), x1)) -> c10(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x1)), MARK(s(U12(z0, z1, z2)))) MARK(plus(s(plus(z0, z1)), x1)) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c10(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(s(z0)), x1)) -> c10(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(0), x1)) -> c10(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(x0), x1)) -> c10(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c10(MARK(s(x0))) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> 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MARK(U11(U11(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U11(U11(x0, z1, z2), x3, x4)) -> c8(MARK(U11(x0, z1, z2))) MARK(U11(U11(0, x1, x2), x3, x4)) -> c8(A__U11(a__U11(0, x1, x2), x3, x4)) MARK(U11(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U11(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U11(U12(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U11(U12(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U11(U12(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U11(U12(x0, z1, z2), x3, x4)) -> c8(MARK(U12(x0, z1, z2))) MARK(U11(U12(0, x1, x2), x3, x4)) -> c8(A__U11(a__U12(0, x1, x2), x3, x4)) MARK(U11(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U11(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U11(plus(x0, plus(z0, z1)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U11(plus(x0, tt), x2, x3)) -> c8(A__U11(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U11(plus(x0, s(z0)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U11(plus(x0, 0), x2, x3)) -> c8(A__U11(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U11(plus(U11(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U11(plus(U12(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U11(plus(plus(z0, z1), x1), x2, x3)) -> c8(A__U11(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U11(plus(tt, x1), x2, x3)) -> c8(A__U11(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U11(plus(s(z0), x1), x2, x3)) -> c8(A__U11(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U11(plus(0, x1), x2, x3)) -> c8(A__U11(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U11(plus(x0, x1), x2, x3)) -> c8(MARK(plus(x0, x1))) MARK(U12(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U12(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U12(U11(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U12(U11(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U12(U11(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U12(U11(x0, z1, z2), x3, x4)) -> c9(MARK(U11(x0, z1, z2))) MARK(U12(U11(0, x1, x2), x3, x4)) -> c9(A__U12(a__U11(0, x1, x2), x3, x4)) MARK(U12(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U12(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U12(U12(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U12(U12(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U12(U12(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U12(U12(x0, z1, z2), x3, x4)) -> c9(MARK(U12(x0, z1, z2))) MARK(U12(U12(0, x1, x2), x3, x4)) -> c9(A__U12(a__U12(0, x1, x2), x3, x4)) MARK(U12(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U12(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U12(plus(x0, plus(z0, z1)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U12(plus(x0, tt), x2, x3)) -> c9(A__U12(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U12(plus(x0, s(z0)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U12(plus(x0, 0), x2, x3)) -> c9(A__U12(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U12(plus(U11(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U12(plus(U12(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U12(plus(plus(z0, z1), x1), x2, x3)) -> c9(A__U12(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U12(plus(tt, x1), x2, x3)) -> c9(A__U12(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U12(plus(s(z0), x1), x2, x3)) -> c9(A__U12(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U12(plus(0, x1), x2, x3)) -> c9(A__U12(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U12(plus(x0, x1), x2, x3)) -> c9(MARK(plus(x0, x1))) MARK(plus(x0, U11(U11(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__U11(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U11(U12(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__U12(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U11(plus(z0, z1), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(tt, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U11(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U11(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(s(z0), U11(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(x0, U11(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U11(x1, x2, x3))) -> c10(A__PLUS(tt, a__U11(mark(x1), x2, x3))) MARK(plus(0, U11(x1, x2, x3))) -> c10(A__PLUS(0, a__U11(mark(x1), x2, x3))) MARK(plus(x0, U12(U11(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__U11(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U12(U12(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__U12(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U12(plus(z0, z1), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(x0)) MARK(plus(x0, U12(tt, x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U12(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U12(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U12(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U12(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U12(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(s(z0), U12(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(x0, U12(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U12(x1, x2, x3))) -> c10(A__PLUS(tt, a__U12(mark(x1), x2, x3))) MARK(plus(0, U12(x1, x2, x3))) -> c10(A__PLUS(0, a__U12(mark(x1), x2, x3))) MARK(plus(x0, plus(x1, U11(z0, z1, z2)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__U11(mark(z0), z1, z2))), MARK(x0)) MARK(plus(x0, plus(x1, U12(z0, z1, z2)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__U12(mark(z0), z1, z2))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(U11(z0, z1, z2), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__U11(mark(z0), z1, z2), mark(x2))), MARK(x0)) MARK(plus(x0, plus(U12(z0, z1, z2), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__U12(mark(z0), z1, z2), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c10(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c10(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c10(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(U11(z0, z1, z2), plus(x1, x2))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), plus(x1, x2))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c10(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))) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c10(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c10(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c10(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(U11(x0, x1, x2), s(z0))) -> c10(A__PLUS(a__U11(mark(x0), x1, x2), s(mark(z0))), MARK(U11(x0, x1, x2))) MARK(plus(U11(x0, x1, x2), 0)) -> c10(A__PLUS(a__U11(mark(x0), x1, x2), 0), MARK(U11(x0, x1, x2))) MARK(plus(U11(x0, z1, z2), x3)) -> c10(A__PLUS(U11(mark(x0), z1, z2), mark(x3)), MARK(U11(x0, z1, z2))) MARK(plus(U11(U11(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(plus(U11(U12(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(plus(U11(plus(z0, z1), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(U11(plus(z0, z1), x1, x2))) MARK(plus(U11(tt, x1, x2), x3)) -> c10(A__PLUS(a__U11(tt, x1, x2), mark(x3)), MARK(U11(tt, x1, x2))) MARK(plus(U11(s(z0), x1, x2), x3)) -> c10(A__PLUS(a__U11(s(mark(z0)), x1, x2), mark(x3)), MARK(U11(s(z0), x1, x2))) MARK(plus(U11(x0, x1, x2), tt)) -> c10(MARK(U11(x0, x1, x2))) MARK(plus(U11(0, x1, x2), x3)) -> c10(A__PLUS(a__U11(0, x1, x2), mark(x3))) MARK(plus(U12(x0, x1, x2), s(z0))) -> c10(A__PLUS(a__U12(mark(x0), x1, x2), s(mark(z0))), MARK(U12(x0, x1, x2))) MARK(plus(U12(x0, x1, x2), 0)) -> c10(A__PLUS(a__U12(mark(x0), x1, x2), 0), MARK(U12(x0, x1, x2))) MARK(plus(U12(x0, z1, z2), x3)) -> c10(A__PLUS(U12(mark(x0), z1, z2), mark(x3)), MARK(U12(x0, z1, z2))) MARK(plus(U12(U11(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(plus(U12(U12(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(plus(U12(plus(z0, z1), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(U12(plus(z0, z1), x1, x2))) MARK(plus(U12(tt, x1, x2), x3)) -> c10(A__PLUS(a__U12(tt, x1, x2), mark(x3)), MARK(U12(tt, x1, x2))) MARK(plus(U12(s(z0), x1, x2), x3)) -> c10(A__PLUS(a__U12(s(mark(z0)), x1, x2), mark(x3)), MARK(U12(s(z0), x1, x2))) MARK(plus(U12(x0, x1, x2), tt)) -> c10(MARK(U12(x0, x1, x2))) MARK(plus(U12(0, x1, x2), x3)) -> c10(A__PLUS(a__U12(0, x1, x2), mark(x3))) MARK(plus(plus(x0, x1), s(z0))) -> c10(A__PLUS(a__plus(mark(x0), mark(x1)), s(mark(z0))), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), 0)) -> c10(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c10(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, U11(z0, z1, z2)), x2)) -> c10(A__PLUS(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), mark(x2)), MARK(plus(x0, U11(z0, z1, z2)))) MARK(plus(plus(x0, U12(z0, z1, z2)), x2)) -> c10(A__PLUS(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), mark(x2)), MARK(plus(x0, U12(z0, z1, z2)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c10(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)) -> c10(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, s(z0)), x2)) -> c10(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(x0, 0), x2)) -> c10(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(U11(z0, z1, z2), x1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(plus(U11(z0, z1, z2), x1))) MARK(plus(plus(U12(z0, z1, z2), x1), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(plus(U12(z0, z1, z2), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c10(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)) -> c10(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(0, x1), x2)) -> c10(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(x0, x1), tt)) -> c10(MARK(plus(x0, x1))) MARK(plus(s(x0), s(z0))) -> c10(A__PLUS(s(mark(x0)), s(mark(z0))), MARK(s(x0))) MARK(plus(s(x0), 0)) -> c10(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(U11(z0, z1, z2)), x1)) -> c10(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x1)), MARK(s(U11(z0, z1, z2)))) MARK(plus(s(U12(z0, z1, z2)), x1)) -> c10(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x1)), MARK(s(U12(z0, z1, z2)))) MARK(plus(s(plus(z0, z1)), x1)) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c10(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(s(z0)), x1)) -> c10(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(0), x1)) -> c10(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(x0), x1)) -> c10(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c10(MARK(s(x0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_1, c9_1, c10_2, c10_1, c11_2, c11_1, c8_2, c9_2 ---------------------------------------- (193) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(tt, x1)) -> c10(A__PLUS(tt, mark(x1))) by MARK(plus(tt, U11(z0, z1, z2))) -> c10(A__PLUS(tt, a__U11(mark(z0), z1, z2))) MARK(plus(tt, U12(z0, z1, z2))) -> c10(A__PLUS(tt, a__U12(mark(z0), z1, z2))) MARK(plus(tt, plus(z0, z1))) -> c10(A__PLUS(tt, a__plus(mark(z0), mark(z1)))) MARK(plus(tt, tt)) -> c10(A__PLUS(tt, tt)) MARK(plus(tt, s(z0))) -> c10(A__PLUS(tt, s(mark(z0)))) MARK(plus(tt, 0)) -> c10(A__PLUS(tt, 0)) ---------------------------------------- (194) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> 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MARK(plus(U11(z0, z1, z2), plus(x1, x2))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), plus(x1, x2))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c10(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))) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c10(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c10(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c10(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(U11(x0, x1, x2), s(z0))) -> c10(A__PLUS(a__U11(mark(x0), x1, x2), s(mark(z0))), MARK(U11(x0, x1, x2))) MARK(plus(U11(x0, x1, x2), 0)) -> c10(A__PLUS(a__U11(mark(x0), x1, x2), 0), MARK(U11(x0, x1, x2))) MARK(plus(U11(x0, z1, z2), x3)) -> c10(A__PLUS(U11(mark(x0), z1, z2), mark(x3)), MARK(U11(x0, z1, z2))) MARK(plus(U11(U11(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(plus(U11(U12(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(plus(U11(plus(z0, z1), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(U11(plus(z0, z1), x1, x2))) MARK(plus(U11(tt, x1, x2), x3)) -> c10(A__PLUS(a__U11(tt, x1, x2), mark(x3)), MARK(U11(tt, x1, x2))) MARK(plus(U11(s(z0), x1, x2), x3)) -> c10(A__PLUS(a__U11(s(mark(z0)), x1, x2), mark(x3)), MARK(U11(s(z0), x1, x2))) MARK(plus(U11(x0, x1, x2), tt)) -> c10(MARK(U11(x0, x1, x2))) MARK(plus(U11(0, x1, x2), x3)) -> c10(A__PLUS(a__U11(0, x1, x2), mark(x3))) MARK(plus(U12(x0, x1, x2), s(z0))) -> c10(A__PLUS(a__U12(mark(x0), x1, x2), s(mark(z0))), MARK(U12(x0, x1, x2))) MARK(plus(U12(x0, x1, x2), 0)) -> c10(A__PLUS(a__U12(mark(x0), x1, x2), 0), MARK(U12(x0, x1, x2))) MARK(plus(U12(x0, z1, z2), x3)) -> c10(A__PLUS(U12(mark(x0), z1, z2), mark(x3)), MARK(U12(x0, z1, z2))) MARK(plus(U12(U11(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(plus(U12(U12(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(plus(U12(plus(z0, z1), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(U12(plus(z0, z1), x1, x2))) MARK(plus(U12(tt, x1, x2), x3)) -> c10(A__PLUS(a__U12(tt, x1, x2), mark(x3)), MARK(U12(tt, x1, x2))) MARK(plus(U12(s(z0), x1, x2), x3)) -> c10(A__PLUS(a__U12(s(mark(z0)), x1, x2), mark(x3)), MARK(U12(s(z0), x1, x2))) MARK(plus(U12(x0, x1, x2), tt)) -> c10(MARK(U12(x0, x1, x2))) MARK(plus(U12(0, x1, x2), x3)) -> c10(A__PLUS(a__U12(0, x1, x2), mark(x3))) MARK(plus(plus(x0, x1), s(z0))) -> c10(A__PLUS(a__plus(mark(x0), mark(x1)), s(mark(z0))), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), 0)) -> c10(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c10(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, U11(z0, z1, z2)), x2)) -> c10(A__PLUS(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), mark(x2)), MARK(plus(x0, U11(z0, z1, z2)))) MARK(plus(plus(x0, U12(z0, z1, z2)), x2)) -> c10(A__PLUS(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), mark(x2)), MARK(plus(x0, U12(z0, z1, z2)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c10(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)) -> c10(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, s(z0)), x2)) -> c10(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(x0, 0), x2)) -> c10(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(U11(z0, z1, z2), x1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(plus(U11(z0, z1, z2), x1))) MARK(plus(plus(U12(z0, z1, z2), x1), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(plus(U12(z0, z1, z2), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c10(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)) -> c10(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(0, x1), x2)) -> c10(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(x0, x1), tt)) -> c10(MARK(plus(x0, x1))) MARK(plus(s(x0), s(z0))) -> c10(A__PLUS(s(mark(x0)), s(mark(z0))), MARK(s(x0))) MARK(plus(s(x0), 0)) -> c10(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(U11(z0, z1, z2)), x1)) -> c10(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x1)), MARK(s(U11(z0, z1, z2)))) MARK(plus(s(U12(z0, z1, z2)), x1)) -> c10(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x1)), MARK(s(U12(z0, z1, z2)))) MARK(plus(s(plus(z0, z1)), x1)) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c10(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(s(z0)), x1)) -> c10(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(0), x1)) -> c10(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(x0), x1)) -> c10(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c10(MARK(s(x0))) MARK(plus(tt, tt)) -> c10(A__PLUS(tt, tt)) MARK(plus(tt, s(z0))) -> c10(A__PLUS(tt, s(mark(z0)))) MARK(plus(tt, 0)) -> c10(A__PLUS(tt, 0)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, 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x3, x4)) -> c9(A__U12(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U12(U11(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U12(U11(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U12(U11(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U12(U11(x0, z1, z2), x3, x4)) -> c9(MARK(U11(x0, z1, z2))) MARK(U12(U11(0, x1, x2), x3, x4)) -> c9(A__U12(a__U11(0, x1, x2), x3, x4)) MARK(U12(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U12(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U12(U12(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U12(U12(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U12(U12(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U12(U12(x0, z1, z2), x3, x4)) -> c9(MARK(U12(x0, z1, z2))) MARK(U12(U12(0, x1, x2), x3, x4)) -> c9(A__U12(a__U12(0, x1, x2), x3, x4)) MARK(U12(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U12(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U12(plus(x0, plus(z0, z1)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U12(plus(x0, tt), x2, x3)) -> c9(A__U12(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U12(plus(x0, s(z0)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U12(plus(x0, 0), x2, x3)) -> c9(A__U12(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U12(plus(U11(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U12(plus(U12(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U12(plus(plus(z0, z1), x1), x2, x3)) -> c9(A__U12(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U12(plus(tt, x1), x2, x3)) -> c9(A__U12(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U12(plus(s(z0), x1), x2, x3)) -> c9(A__U12(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U12(plus(0, x1), x2, x3)) -> c9(A__U12(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U12(plus(x0, x1), x2, x3)) -> c9(MARK(plus(x0, x1))) MARK(plus(x0, U11(U11(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__U11(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U11(U12(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__U12(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U11(plus(z0, z1), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(tt, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U11(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U11(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(s(z0), U11(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(x0, U11(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U11(x1, x2, x3))) -> c10(A__PLUS(tt, a__U11(mark(x1), x2, x3))) MARK(plus(0, U11(x1, x2, x3))) -> c10(A__PLUS(0, a__U11(mark(x1), x2, x3))) MARK(plus(x0, U12(U11(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__U11(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U12(U12(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__U12(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U12(plus(z0, z1), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(x0)) MARK(plus(x0, U12(tt, x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U12(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U12(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U12(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U12(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U12(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(s(z0), U12(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(x0, U12(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U12(x1, x2, x3))) -> c10(A__PLUS(tt, a__U12(mark(x1), x2, x3))) MARK(plus(0, U12(x1, x2, x3))) -> c10(A__PLUS(0, a__U12(mark(x1), x2, x3))) MARK(plus(x0, plus(x1, U11(z0, z1, z2)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__U11(mark(z0), z1, z2))), MARK(x0)) MARK(plus(x0, plus(x1, U12(z0, z1, z2)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__U12(mark(z0), z1, z2))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(U11(z0, z1, z2), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__U11(mark(z0), z1, z2), mark(x2))), MARK(x0)) MARK(plus(x0, plus(U12(z0, z1, z2), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__U12(mark(z0), z1, z2), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c10(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c10(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c10(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(U11(z0, z1, z2), plus(x1, x2))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), plus(x1, x2))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c10(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))) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c10(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c10(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c10(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(U11(x0, x1, x2), s(z0))) -> c10(A__PLUS(a__U11(mark(x0), x1, x2), s(mark(z0))), MARK(U11(x0, x1, x2))) MARK(plus(U11(x0, x1, x2), 0)) -> c10(A__PLUS(a__U11(mark(x0), x1, x2), 0), MARK(U11(x0, x1, x2))) MARK(plus(U11(x0, z1, z2), x3)) -> c10(A__PLUS(U11(mark(x0), z1, z2), mark(x3)), MARK(U11(x0, z1, z2))) MARK(plus(U11(U11(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(plus(U11(U12(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(plus(U11(plus(z0, z1), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(U11(plus(z0, z1), x1, x2))) MARK(plus(U11(tt, x1, x2), x3)) -> c10(A__PLUS(a__U11(tt, x1, x2), mark(x3)), MARK(U11(tt, x1, x2))) MARK(plus(U11(s(z0), x1, x2), x3)) -> c10(A__PLUS(a__U11(s(mark(z0)), x1, x2), mark(x3)), MARK(U11(s(z0), x1, x2))) MARK(plus(U11(x0, x1, x2), tt)) -> c10(MARK(U11(x0, x1, x2))) MARK(plus(U11(0, x1, x2), x3)) -> c10(A__PLUS(a__U11(0, x1, x2), mark(x3))) MARK(plus(U12(x0, x1, x2), s(z0))) -> c10(A__PLUS(a__U12(mark(x0), x1, x2), s(mark(z0))), MARK(U12(x0, x1, x2))) MARK(plus(U12(x0, x1, x2), 0)) -> c10(A__PLUS(a__U12(mark(x0), x1, x2), 0), MARK(U12(x0, x1, x2))) MARK(plus(U12(x0, z1, z2), x3)) -> c10(A__PLUS(U12(mark(x0), z1, z2), mark(x3)), MARK(U12(x0, z1, z2))) MARK(plus(U12(U11(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(plus(U12(U12(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(plus(U12(plus(z0, z1), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(U12(plus(z0, z1), x1, x2))) MARK(plus(U12(tt, x1, x2), x3)) -> c10(A__PLUS(a__U12(tt, x1, x2), mark(x3)), MARK(U12(tt, x1, x2))) MARK(plus(U12(s(z0), x1, x2), x3)) -> c10(A__PLUS(a__U12(s(mark(z0)), x1, x2), mark(x3)), MARK(U12(s(z0), x1, x2))) MARK(plus(U12(x0, x1, x2), tt)) -> c10(MARK(U12(x0, x1, x2))) MARK(plus(U12(0, x1, x2), x3)) -> c10(A__PLUS(a__U12(0, x1, x2), mark(x3))) MARK(plus(plus(x0, x1), s(z0))) -> c10(A__PLUS(a__plus(mark(x0), mark(x1)), s(mark(z0))), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), 0)) -> c10(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c10(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, U11(z0, z1, z2)), x2)) -> c10(A__PLUS(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), mark(x2)), MARK(plus(x0, U11(z0, z1, z2)))) MARK(plus(plus(x0, U12(z0, z1, z2)), x2)) -> c10(A__PLUS(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), mark(x2)), MARK(plus(x0, U12(z0, z1, z2)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c10(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)) -> c10(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, s(z0)), x2)) -> c10(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(x0, 0), x2)) -> c10(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(U11(z0, z1, z2), x1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(plus(U11(z0, z1, z2), x1))) MARK(plus(plus(U12(z0, z1, z2), x1), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(plus(U12(z0, z1, z2), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c10(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)) -> c10(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(0, x1), x2)) -> c10(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(x0, x1), tt)) -> c10(MARK(plus(x0, x1))) MARK(plus(s(x0), s(z0))) -> c10(A__PLUS(s(mark(x0)), s(mark(z0))), MARK(s(x0))) MARK(plus(s(x0), 0)) -> c10(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(U11(z0, z1, z2)), x1)) -> c10(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x1)), MARK(s(U11(z0, z1, z2)))) MARK(plus(s(U12(z0, z1, z2)), x1)) -> c10(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x1)), MARK(s(U12(z0, z1, z2)))) MARK(plus(s(plus(z0, z1)), x1)) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c10(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(s(z0)), x1)) -> c10(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(0), x1)) -> c10(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(x0), x1)) -> c10(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c10(MARK(s(x0))) MARK(plus(tt, tt)) -> c10(A__PLUS(tt, tt)) MARK(plus(tt, s(z0))) -> c10(A__PLUS(tt, s(mark(z0)))) MARK(plus(tt, 0)) -> c10(A__PLUS(tt, 0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_1, c9_1, c10_2, c10_1, c11_2, c11_1, c8_2, c9_2 ---------------------------------------- (195) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(plus(tt, tt)) -> c10(A__PLUS(tt, tt)) ---------------------------------------- (196) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> 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MARK(U11(U12(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U11(U12(x0, z1, z2), x3, x4)) -> c8(MARK(U12(x0, z1, z2))) MARK(U11(U12(0, x1, x2), x3, x4)) -> c8(A__U11(a__U12(0, x1, x2), x3, x4)) MARK(U11(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U11(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U11(plus(x0, plus(z0, z1)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U11(plus(x0, tt), x2, x3)) -> c8(A__U11(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U11(plus(x0, s(z0)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U11(plus(x0, 0), x2, x3)) -> c8(A__U11(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U11(plus(U11(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U11(plus(U12(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U11(plus(plus(z0, z1), x1), x2, x3)) -> c8(A__U11(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U11(plus(tt, x1), x2, x3)) -> c8(A__U11(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U11(plus(s(z0), x1), x2, x3)) -> c8(A__U11(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U11(plus(0, x1), x2, x3)) -> c8(A__U11(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U11(plus(x0, x1), x2, x3)) -> c8(MARK(plus(x0, x1))) MARK(U12(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U12(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U12(U11(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U12(U11(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U12(U11(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U12(U11(x0, z1, z2), x3, x4)) -> c9(MARK(U11(x0, z1, z2))) MARK(U12(U11(0, x1, x2), x3, x4)) -> c9(A__U12(a__U11(0, x1, x2), x3, x4)) MARK(U12(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U12(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U12(U12(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U12(U12(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U12(U12(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U12(U12(x0, z1, z2), x3, x4)) -> c9(MARK(U12(x0, z1, z2))) MARK(U12(U12(0, x1, x2), x3, x4)) -> c9(A__U12(a__U12(0, x1, x2), x3, x4)) MARK(U12(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U12(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U12(plus(x0, plus(z0, z1)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U12(plus(x0, tt), x2, x3)) -> c9(A__U12(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U12(plus(x0, s(z0)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U12(plus(x0, 0), x2, x3)) -> c9(A__U12(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U12(plus(U11(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U12(plus(U12(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U12(plus(plus(z0, z1), x1), x2, x3)) -> c9(A__U12(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U12(plus(tt, x1), x2, x3)) -> c9(A__U12(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U12(plus(s(z0), x1), x2, x3)) -> c9(A__U12(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U12(plus(0, x1), x2, x3)) -> c9(A__U12(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U12(plus(x0, x1), x2, x3)) -> c9(MARK(plus(x0, x1))) MARK(plus(x0, U11(U11(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__U11(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U11(U12(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__U12(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U11(plus(z0, z1), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(tt, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U11(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U11(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(s(z0), U11(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(x0, U11(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U11(x1, x2, x3))) -> c10(A__PLUS(tt, a__U11(mark(x1), x2, x3))) MARK(plus(0, U11(x1, x2, x3))) -> c10(A__PLUS(0, a__U11(mark(x1), x2, x3))) MARK(plus(x0, U12(U11(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__U11(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U12(U12(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__U12(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U12(plus(z0, z1), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(x0)) MARK(plus(x0, U12(tt, x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U12(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U12(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U12(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U12(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U12(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(s(z0), U12(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(x0, U12(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U12(x1, x2, x3))) -> c10(A__PLUS(tt, a__U12(mark(x1), x2, x3))) MARK(plus(0, U12(x1, x2, x3))) -> c10(A__PLUS(0, a__U12(mark(x1), x2, x3))) MARK(plus(x0, plus(x1, U11(z0, z1, z2)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__U11(mark(z0), z1, z2))), MARK(x0)) MARK(plus(x0, plus(x1, U12(z0, z1, z2)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__U12(mark(z0), z1, z2))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(U11(z0, z1, z2), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__U11(mark(z0), z1, z2), mark(x2))), MARK(x0)) MARK(plus(x0, plus(U12(z0, z1, z2), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__U12(mark(z0), z1, z2), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c10(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c10(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c10(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(U11(z0, z1, z2), plus(x1, x2))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), plus(x1, x2))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c10(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))) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c10(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c10(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c10(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(U11(x0, x1, x2), s(z0))) -> c10(A__PLUS(a__U11(mark(x0), x1, x2), s(mark(z0))), MARK(U11(x0, x1, x2))) MARK(plus(U11(x0, x1, x2), 0)) -> c10(A__PLUS(a__U11(mark(x0), x1, x2), 0), MARK(U11(x0, x1, x2))) MARK(plus(U11(x0, z1, z2), x3)) -> c10(A__PLUS(U11(mark(x0), z1, z2), mark(x3)), MARK(U11(x0, z1, z2))) MARK(plus(U11(U11(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(plus(U11(U12(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(plus(U11(plus(z0, z1), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(U11(plus(z0, z1), x1, x2))) MARK(plus(U11(tt, x1, x2), x3)) -> c10(A__PLUS(a__U11(tt, x1, x2), mark(x3)), MARK(U11(tt, x1, x2))) MARK(plus(U11(s(z0), x1, x2), x3)) -> c10(A__PLUS(a__U11(s(mark(z0)), x1, x2), mark(x3)), MARK(U11(s(z0), x1, x2))) MARK(plus(U11(x0, x1, x2), tt)) -> c10(MARK(U11(x0, x1, x2))) MARK(plus(U11(0, x1, x2), x3)) -> c10(A__PLUS(a__U11(0, x1, x2), mark(x3))) MARK(plus(U12(x0, x1, x2), s(z0))) -> c10(A__PLUS(a__U12(mark(x0), x1, x2), s(mark(z0))), MARK(U12(x0, x1, x2))) MARK(plus(U12(x0, x1, x2), 0)) -> c10(A__PLUS(a__U12(mark(x0), x1, x2), 0), MARK(U12(x0, x1, x2))) MARK(plus(U12(x0, z1, z2), x3)) -> c10(A__PLUS(U12(mark(x0), z1, z2), mark(x3)), MARK(U12(x0, z1, z2))) MARK(plus(U12(U11(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(plus(U12(U12(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(plus(U12(plus(z0, z1), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(U12(plus(z0, z1), x1, x2))) MARK(plus(U12(tt, x1, x2), x3)) -> c10(A__PLUS(a__U12(tt, x1, x2), mark(x3)), MARK(U12(tt, x1, x2))) MARK(plus(U12(s(z0), x1, x2), x3)) -> c10(A__PLUS(a__U12(s(mark(z0)), x1, x2), mark(x3)), MARK(U12(s(z0), x1, x2))) MARK(plus(U12(x0, x1, x2), tt)) -> c10(MARK(U12(x0, x1, x2))) MARK(plus(U12(0, x1, x2), x3)) -> c10(A__PLUS(a__U12(0, x1, x2), mark(x3))) MARK(plus(plus(x0, x1), s(z0))) -> c10(A__PLUS(a__plus(mark(x0), mark(x1)), s(mark(z0))), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), 0)) -> c10(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c10(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, U11(z0, z1, z2)), x2)) -> c10(A__PLUS(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), mark(x2)), MARK(plus(x0, U11(z0, z1, z2)))) MARK(plus(plus(x0, U12(z0, z1, z2)), x2)) -> c10(A__PLUS(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), mark(x2)), MARK(plus(x0, U12(z0, z1, z2)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c10(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)) -> c10(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, s(z0)), x2)) -> c10(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(x0, 0), x2)) -> c10(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(U11(z0, z1, z2), x1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(plus(U11(z0, z1, z2), x1))) MARK(plus(plus(U12(z0, z1, z2), x1), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(plus(U12(z0, z1, z2), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c10(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)) -> c10(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(0, x1), x2)) -> c10(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(x0, x1), tt)) -> c10(MARK(plus(x0, x1))) MARK(plus(s(x0), s(z0))) -> c10(A__PLUS(s(mark(x0)), s(mark(z0))), MARK(s(x0))) MARK(plus(s(x0), 0)) -> c10(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(U11(z0, z1, z2)), x1)) -> c10(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x1)), MARK(s(U11(z0, z1, z2)))) MARK(plus(s(U12(z0, z1, z2)), x1)) -> c10(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x1)), MARK(s(U12(z0, z1, z2)))) MARK(plus(s(plus(z0, z1)), x1)) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c10(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(s(z0)), x1)) -> c10(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(0), x1)) -> c10(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(x0), x1)) -> c10(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c10(MARK(s(x0))) MARK(plus(tt, s(z0))) -> c10(A__PLUS(tt, s(mark(z0)))) MARK(plus(tt, 0)) -> c10(A__PLUS(tt, 0)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), 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U11(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(x0, U11(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U11(x1, x2, x3))) -> c10(A__PLUS(tt, a__U11(mark(x1), x2, x3))) MARK(plus(0, U11(x1, x2, x3))) -> c10(A__PLUS(0, a__U11(mark(x1), x2, x3))) MARK(plus(x0, U12(U11(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__U11(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U12(U12(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__U12(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U12(plus(z0, z1), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(x0)) MARK(plus(x0, U12(tt, x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U12(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U12(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U12(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U12(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U12(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(s(z0), U12(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(x0, U12(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U12(x1, x2, x3))) -> c10(A__PLUS(tt, a__U12(mark(x1), x2, x3))) MARK(plus(0, U12(x1, x2, x3))) -> c10(A__PLUS(0, a__U12(mark(x1), x2, x3))) MARK(plus(x0, plus(x1, U11(z0, z1, z2)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__U11(mark(z0), z1, z2))), MARK(x0)) MARK(plus(x0, plus(x1, U12(z0, z1, z2)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__U12(mark(z0), z1, z2))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(U11(z0, z1, z2), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__U11(mark(z0), z1, z2), mark(x2))), MARK(x0)) MARK(plus(x0, plus(U12(z0, z1, z2), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__U12(mark(z0), z1, z2), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c10(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c10(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c10(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(U11(z0, z1, z2), plus(x1, x2))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), plus(x1, x2))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c10(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))) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c10(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c10(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c10(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(U11(x0, x1, x2), s(z0))) -> c10(A__PLUS(a__U11(mark(x0), x1, x2), s(mark(z0))), MARK(U11(x0, x1, x2))) MARK(plus(U11(x0, x1, x2), 0)) -> c10(A__PLUS(a__U11(mark(x0), x1, x2), 0), MARK(U11(x0, x1, x2))) MARK(plus(U11(x0, z1, z2), x3)) -> c10(A__PLUS(U11(mark(x0), z1, z2), mark(x3)), MARK(U11(x0, z1, z2))) MARK(plus(U11(U11(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(plus(U11(U12(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(plus(U11(plus(z0, z1), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(U11(plus(z0, z1), x1, x2))) MARK(plus(U11(tt, x1, x2), x3)) -> c10(A__PLUS(a__U11(tt, x1, x2), mark(x3)), MARK(U11(tt, x1, x2))) MARK(plus(U11(s(z0), x1, x2), x3)) -> c10(A__PLUS(a__U11(s(mark(z0)), x1, x2), mark(x3)), MARK(U11(s(z0), x1, x2))) MARK(plus(U11(x0, x1, x2), tt)) -> c10(MARK(U11(x0, x1, x2))) MARK(plus(U11(0, x1, x2), x3)) -> c10(A__PLUS(a__U11(0, x1, x2), mark(x3))) MARK(plus(U12(x0, x1, x2), s(z0))) -> c10(A__PLUS(a__U12(mark(x0), x1, x2), s(mark(z0))), MARK(U12(x0, x1, x2))) MARK(plus(U12(x0, x1, x2), 0)) -> c10(A__PLUS(a__U12(mark(x0), x1, x2), 0), MARK(U12(x0, x1, x2))) MARK(plus(U12(x0, z1, z2), x3)) -> c10(A__PLUS(U12(mark(x0), z1, z2), mark(x3)), MARK(U12(x0, z1, z2))) MARK(plus(U12(U11(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(plus(U12(U12(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(plus(U12(plus(z0, z1), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(U12(plus(z0, z1), x1, x2))) MARK(plus(U12(tt, x1, x2), x3)) -> c10(A__PLUS(a__U12(tt, x1, x2), mark(x3)), MARK(U12(tt, x1, x2))) MARK(plus(U12(s(z0), x1, x2), x3)) -> c10(A__PLUS(a__U12(s(mark(z0)), x1, x2), mark(x3)), MARK(U12(s(z0), x1, x2))) MARK(plus(U12(x0, x1, x2), tt)) -> c10(MARK(U12(x0, x1, x2))) MARK(plus(U12(0, x1, x2), x3)) -> c10(A__PLUS(a__U12(0, x1, x2), mark(x3))) MARK(plus(plus(x0, x1), s(z0))) -> c10(A__PLUS(a__plus(mark(x0), mark(x1)), s(mark(z0))), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), 0)) -> c10(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c10(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, U11(z0, z1, z2)), x2)) -> c10(A__PLUS(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), mark(x2)), MARK(plus(x0, U11(z0, z1, z2)))) MARK(plus(plus(x0, U12(z0, z1, z2)), x2)) -> c10(A__PLUS(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), mark(x2)), MARK(plus(x0, U12(z0, z1, z2)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c10(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)) -> c10(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, s(z0)), x2)) -> c10(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(x0, 0), x2)) -> c10(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(U11(z0, z1, z2), x1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(plus(U11(z0, z1, z2), x1))) MARK(plus(plus(U12(z0, z1, z2), x1), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(plus(U12(z0, z1, z2), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c10(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)) -> c10(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(0, x1), x2)) -> c10(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(x0, x1), tt)) -> c10(MARK(plus(x0, x1))) MARK(plus(s(x0), s(z0))) -> c10(A__PLUS(s(mark(x0)), s(mark(z0))), MARK(s(x0))) MARK(plus(s(x0), 0)) -> c10(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(U11(z0, z1, z2)), x1)) -> c10(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x1)), MARK(s(U11(z0, z1, z2)))) MARK(plus(s(U12(z0, z1, z2)), x1)) -> c10(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x1)), MARK(s(U12(z0, z1, z2)))) MARK(plus(s(plus(z0, z1)), x1)) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c10(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(s(z0)), x1)) -> c10(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(0), x1)) -> c10(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(x0), x1)) -> c10(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c10(MARK(s(x0))) MARK(plus(tt, s(z0))) -> c10(A__PLUS(tt, s(mark(z0)))) MARK(plus(tt, 0)) -> c10(A__PLUS(tt, 0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_1, c9_1, c10_2, c10_1, c11_2, c11_1, c8_2, c9_2 ---------------------------------------- (197) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(0, x1)) -> c10(A__PLUS(0, mark(x1))) by MARK(plus(0, U11(z0, z1, z2))) -> c10(A__PLUS(0, a__U11(mark(z0), z1, z2))) MARK(plus(0, U12(z0, z1, z2))) -> c10(A__PLUS(0, a__U12(mark(z0), z1, z2))) MARK(plus(0, plus(z0, z1))) -> c10(A__PLUS(0, a__plus(mark(z0), mark(z1)))) MARK(plus(0, tt)) -> c10(A__PLUS(0, tt)) MARK(plus(0, s(z0))) -> c10(A__PLUS(0, s(mark(z0)))) MARK(plus(0, 0)) -> c10(A__PLUS(0, 0)) ---------------------------------------- (198) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, 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z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), 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c10(A__PLUS(mark(x0), a__U12(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U12(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U12(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U12(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U12(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(s(z0), U12(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(x0, U12(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U12(x1, x2, x3))) -> c10(A__PLUS(tt, a__U12(mark(x1), x2, x3))) MARK(plus(0, U12(x1, x2, x3))) -> c10(A__PLUS(0, a__U12(mark(x1), x2, x3))) MARK(plus(x0, plus(x1, U11(z0, z1, z2)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__U11(mark(z0), z1, z2))), MARK(x0)) MARK(plus(x0, 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c10(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c10(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(U11(z0, z1, z2), plus(x1, x2))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), plus(x1, x2))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c10(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))) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c10(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c10(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c10(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(U11(x0, x1, x2), s(z0))) -> c10(A__PLUS(a__U11(mark(x0), x1, x2), s(mark(z0))), MARK(U11(x0, x1, x2))) MARK(plus(U11(x0, x1, x2), 0)) -> c10(A__PLUS(a__U11(mark(x0), x1, x2), 0), MARK(U11(x0, x1, x2))) MARK(plus(U11(x0, z1, z2), x3)) -> c10(A__PLUS(U11(mark(x0), z1, z2), mark(x3)), MARK(U11(x0, z1, z2))) MARK(plus(U11(U11(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(plus(U11(U12(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(plus(U11(plus(z0, z1), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(U11(plus(z0, z1), x1, x2))) MARK(plus(U11(tt, x1, x2), x3)) -> c10(A__PLUS(a__U11(tt, x1, x2), mark(x3)), MARK(U11(tt, x1, x2))) MARK(plus(U11(s(z0), x1, x2), x3)) -> c10(A__PLUS(a__U11(s(mark(z0)), x1, x2), mark(x3)), MARK(U11(s(z0), x1, x2))) MARK(plus(U11(x0, x1, x2), tt)) -> c10(MARK(U11(x0, x1, x2))) MARK(plus(U11(0, x1, x2), x3)) -> c10(A__PLUS(a__U11(0, x1, x2), mark(x3))) MARK(plus(U12(x0, x1, 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c10(MARK(U12(x0, x1, x2))) MARK(plus(U12(0, x1, x2), x3)) -> c10(A__PLUS(a__U12(0, x1, x2), mark(x3))) MARK(plus(plus(x0, x1), s(z0))) -> c10(A__PLUS(a__plus(mark(x0), mark(x1)), s(mark(z0))), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), 0)) -> c10(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c10(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, U11(z0, z1, z2)), x2)) -> c10(A__PLUS(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), mark(x2)), MARK(plus(x0, U11(z0, z1, z2)))) MARK(plus(plus(x0, U12(z0, z1, z2)), x2)) -> c10(A__PLUS(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), mark(x2)), MARK(plus(x0, U12(z0, z1, z2)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c10(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)) -> c10(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, s(z0)), x2)) -> c10(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(x0, 0), x2)) -> c10(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(U11(z0, z1, z2), x1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(plus(U11(z0, z1, z2), x1))) MARK(plus(plus(U12(z0, z1, z2), x1), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(plus(U12(z0, z1, z2), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c10(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)) -> c10(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(0, x1), x2)) -> c10(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(x0, x1), tt)) -> c10(MARK(plus(x0, x1))) MARK(plus(s(x0), s(z0))) -> c10(A__PLUS(s(mark(x0)), s(mark(z0))), MARK(s(x0))) MARK(plus(s(x0), 0)) -> c10(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(U11(z0, z1, z2)), x1)) -> c10(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x1)), MARK(s(U11(z0, z1, z2)))) MARK(plus(s(U12(z0, z1, z2)), x1)) -> c10(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x1)), MARK(s(U12(z0, z1, z2)))) MARK(plus(s(plus(z0, z1)), x1)) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c10(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(s(z0)), x1)) -> c10(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(0), x1)) -> c10(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(x0), x1)) -> c10(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c10(MARK(s(x0))) MARK(plus(tt, s(z0))) -> c10(A__PLUS(tt, s(mark(z0)))) MARK(plus(tt, 0)) -> c10(A__PLUS(tt, 0)) MARK(plus(0, tt)) -> c10(A__PLUS(0, tt)) MARK(plus(0, s(z0))) -> c10(A__PLUS(0, s(mark(z0)))) MARK(plus(0, 0)) -> c10(A__PLUS(0, 0)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U12(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c3(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c3(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U12(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U12(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U12(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, 0) -> c3(A__PLUS(0, 0)) MARK(U11(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), 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x2), s(z0))) -> c10(A__PLUS(a__U12(mark(x0), x1, x2), s(mark(z0))), MARK(U12(x0, x1, x2))) MARK(plus(U12(x0, x1, x2), 0)) -> c10(A__PLUS(a__U12(mark(x0), x1, x2), 0), MARK(U12(x0, x1, x2))) MARK(plus(U12(x0, z1, z2), x3)) -> c10(A__PLUS(U12(mark(x0), z1, z2), mark(x3)), MARK(U12(x0, z1, z2))) MARK(plus(U12(U11(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(plus(U12(U12(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(plus(U12(plus(z0, z1), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(U12(plus(z0, z1), x1, x2))) MARK(plus(U12(tt, x1, x2), x3)) -> c10(A__PLUS(a__U12(tt, x1, x2), mark(x3)), MARK(U12(tt, x1, x2))) MARK(plus(U12(s(z0), x1, x2), x3)) -> c10(A__PLUS(a__U12(s(mark(z0)), x1, x2), mark(x3)), MARK(U12(s(z0), x1, x2))) MARK(plus(U12(x0, x1, x2), tt)) -> 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c10(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(x0, 0), x2)) -> c10(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(U11(z0, z1, z2), x1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(plus(U11(z0, z1, z2), x1))) MARK(plus(plus(U12(z0, z1, z2), x1), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(plus(U12(z0, z1, z2), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c10(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)) -> c10(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(0, x1), x2)) -> c10(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(x0, x1), tt)) -> c10(MARK(plus(x0, x1))) MARK(plus(s(x0), s(z0))) -> c10(A__PLUS(s(mark(x0)), s(mark(z0))), MARK(s(x0))) MARK(plus(s(x0), 0)) -> c10(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(U11(z0, z1, z2)), x1)) -> c10(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x1)), MARK(s(U11(z0, z1, z2)))) MARK(plus(s(U12(z0, z1, z2)), x1)) -> c10(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x1)), MARK(s(U12(z0, z1, z2)))) MARK(plus(s(plus(z0, z1)), x1)) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c10(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(s(z0)), x1)) -> c10(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(0), x1)) -> c10(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(x0), x1)) -> c10(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c10(MARK(s(x0))) MARK(plus(tt, s(z0))) -> c10(A__PLUS(tt, s(mark(z0)))) MARK(plus(tt, 0)) -> c10(A__PLUS(tt, 0)) MARK(plus(0, tt)) -> c10(A__PLUS(0, tt)) MARK(plus(0, s(z0))) -> c10(A__PLUS(0, s(mark(z0)))) MARK(plus(0, 0)) -> c10(A__PLUS(0, 0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_1, c9_1, c10_2, c10_1, c11_2, c11_1, c8_2, c9_2 ---------------------------------------- (199) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(plus(0, tt)) -> c10(A__PLUS(0, tt)) ---------------------------------------- (200) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U12(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c3(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c3(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U12(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U12(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U12(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, 0) -> c3(A__PLUS(0, 0)) MARK(U11(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U11(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U11(U11(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U11(U11(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U11(U11(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U11(U11(x0, z1, z2), x3, x4)) -> c8(MARK(U11(x0, z1, z2))) MARK(U11(U11(0, x1, x2), x3, x4)) -> c8(A__U11(a__U11(0, x1, x2), x3, x4)) MARK(U11(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U11(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U11(U12(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U11(U12(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U11(U12(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U11(U12(x0, z1, z2), x3, x4)) -> c8(MARK(U12(x0, z1, z2))) MARK(U11(U12(0, x1, x2), x3, x4)) -> c8(A__U11(a__U12(0, x1, x2), x3, x4)) MARK(U11(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U11(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U11(plus(x0, plus(z0, z1)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U11(plus(x0, tt), x2, x3)) -> c8(A__U11(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U11(plus(x0, s(z0)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U11(plus(x0, 0), x2, x3)) -> c8(A__U11(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U11(plus(U11(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U11(plus(U12(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U11(plus(plus(z0, z1), x1), x2, x3)) -> c8(A__U11(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U11(plus(tt, x1), x2, x3)) -> c8(A__U11(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U11(plus(s(z0), x1), x2, x3)) -> c8(A__U11(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U11(plus(0, x1), x2, x3)) -> c8(A__U11(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U11(plus(x0, x1), x2, x3)) -> c8(MARK(plus(x0, 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c9(A__U12(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U12(U12(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U12(U12(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U12(U12(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U12(U12(x0, z1, z2), x3, x4)) -> c9(MARK(U12(x0, z1, z2))) MARK(U12(U12(0, x1, x2), x3, x4)) -> c9(A__U12(a__U12(0, x1, x2), x3, x4)) MARK(U12(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U12(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U12(plus(x0, plus(z0, z1)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U12(plus(x0, tt), x2, x3)) -> c9(A__U12(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U12(plus(x0, s(z0)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U12(plus(x0, 0), x2, x3)) -> c9(A__U12(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U12(plus(U11(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U12(plus(U12(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U12(plus(plus(z0, z1), x1), x2, x3)) -> c9(A__U12(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U12(plus(tt, x1), x2, x3)) -> c9(A__U12(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U12(plus(s(z0), x1), x2, x3)) -> c9(A__U12(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U12(plus(0, x1), x2, 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c10(A__PLUS(mark(x0), a__U12(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U12(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U12(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U12(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U12(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(s(z0), U12(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(x0, U12(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U12(x1, x2, x3))) -> c10(A__PLUS(tt, a__U12(mark(x1), x2, x3))) MARK(plus(0, U12(x1, x2, x3))) -> c10(A__PLUS(0, a__U12(mark(x1), x2, x3))) MARK(plus(x0, plus(x1, U11(z0, z1, z2)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__U11(mark(z0), z1, z2))), MARK(x0)) MARK(plus(x0, 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c10(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c10(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(U11(z0, z1, z2), plus(x1, x2))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), plus(x1, x2))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c10(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))) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c10(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c10(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c10(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(U11(x0, x1, x2), s(z0))) -> c10(A__PLUS(a__U11(mark(x0), x1, x2), s(mark(z0))), MARK(U11(x0, x1, x2))) MARK(plus(U11(x0, x1, x2), 0)) -> c10(A__PLUS(a__U11(mark(x0), x1, x2), 0), MARK(U11(x0, x1, x2))) MARK(plus(U11(x0, z1, z2), x3)) -> c10(A__PLUS(U11(mark(x0), z1, z2), mark(x3)), MARK(U11(x0, z1, z2))) MARK(plus(U11(U11(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(plus(U11(U12(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(plus(U11(plus(z0, z1), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(U11(plus(z0, z1), x1, x2))) MARK(plus(U11(tt, x1, x2), x3)) -> c10(A__PLUS(a__U11(tt, x1, x2), mark(x3)), MARK(U11(tt, x1, x2))) MARK(plus(U11(s(z0), x1, x2), x3)) -> c10(A__PLUS(a__U11(s(mark(z0)), x1, x2), mark(x3)), MARK(U11(s(z0), x1, x2))) MARK(plus(U11(x0, x1, x2), tt)) -> c10(MARK(U11(x0, x1, x2))) MARK(plus(U11(0, x1, x2), x3)) -> c10(A__PLUS(a__U11(0, x1, x2), mark(x3))) MARK(plus(U12(x0, x1, x2), s(z0))) -> c10(A__PLUS(a__U12(mark(x0), x1, x2), s(mark(z0))), MARK(U12(x0, x1, x2))) MARK(plus(U12(x0, x1, x2), 0)) -> c10(A__PLUS(a__U12(mark(x0), x1, x2), 0), MARK(U12(x0, x1, x2))) MARK(plus(U12(x0, z1, z2), x3)) -> c10(A__PLUS(U12(mark(x0), z1, z2), mark(x3)), MARK(U12(x0, z1, z2))) MARK(plus(U12(U11(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(plus(U12(U12(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(plus(U12(plus(z0, z1), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(U12(plus(z0, z1), x1, x2))) MARK(plus(U12(tt, x1, x2), x3)) -> c10(A__PLUS(a__U12(tt, x1, x2), mark(x3)), MARK(U12(tt, x1, x2))) MARK(plus(U12(s(z0), x1, x2), x3)) -> c10(A__PLUS(a__U12(s(mark(z0)), x1, x2), mark(x3)), MARK(U12(s(z0), x1, x2))) MARK(plus(U12(x0, x1, x2), tt)) -> c10(MARK(U12(x0, x1, x2))) MARK(plus(U12(0, x1, x2), x3)) -> c10(A__PLUS(a__U12(0, x1, x2), mark(x3))) MARK(plus(plus(x0, x1), s(z0))) -> c10(A__PLUS(a__plus(mark(x0), mark(x1)), s(mark(z0))), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), 0)) -> c10(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c10(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, U11(z0, z1, z2)), x2)) -> c10(A__PLUS(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), mark(x2)), MARK(plus(x0, U11(z0, z1, z2)))) MARK(plus(plus(x0, U12(z0, z1, z2)), x2)) -> c10(A__PLUS(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), mark(x2)), MARK(plus(x0, U12(z0, z1, z2)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c10(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)) -> c10(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, s(z0)), x2)) -> c10(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(x0, 0), x2)) -> c10(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(U11(z0, z1, z2), x1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(plus(U11(z0, z1, z2), x1))) MARK(plus(plus(U12(z0, z1, z2), x1), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(plus(U12(z0, z1, z2), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c10(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)) -> c10(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(0, x1), x2)) -> c10(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(x0, x1), tt)) -> c10(MARK(plus(x0, x1))) MARK(plus(s(x0), s(z0))) -> c10(A__PLUS(s(mark(x0)), s(mark(z0))), MARK(s(x0))) MARK(plus(s(x0), 0)) -> c10(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(U11(z0, z1, z2)), x1)) -> c10(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x1)), MARK(s(U11(z0, z1, z2)))) MARK(plus(s(U12(z0, z1, z2)), x1)) -> c10(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x1)), MARK(s(U12(z0, z1, z2)))) MARK(plus(s(plus(z0, z1)), x1)) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c10(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(s(z0)), x1)) -> c10(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(0), x1)) -> c10(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(x0), x1)) -> c10(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c10(MARK(s(x0))) MARK(plus(tt, s(z0))) -> c10(A__PLUS(tt, s(mark(z0)))) MARK(plus(tt, 0)) -> c10(A__PLUS(tt, 0)) MARK(plus(0, s(z0))) -> c10(A__PLUS(0, s(mark(z0)))) MARK(plus(0, 0)) -> c10(A__PLUS(0, 0)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, 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MARK(plus(x0, plus(z0, z1)))) MARK(U12(plus(x0, tt), x2, x3)) -> c9(A__U12(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U12(plus(x0, s(z0)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U12(plus(x0, 0), x2, x3)) -> c9(A__U12(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U12(plus(U11(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U12(plus(U12(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U12(plus(plus(z0, z1), x1), x2, x3)) -> c9(A__U12(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U12(plus(tt, x1), x2, x3)) -> c9(A__U12(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U12(plus(s(z0), x1), x2, x3)) -> c9(A__U12(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U12(plus(0, x1), x2, x3)) -> c9(A__U12(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U12(plus(x0, x1), x2, x3)) -> c9(MARK(plus(x0, x1))) MARK(plus(x0, U11(U11(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__U11(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U11(U12(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__U12(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U11(plus(z0, z1), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(tt, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U11(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U11(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(s(z0), U11(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(x0, U11(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U11(x1, x2, x3))) -> c10(A__PLUS(tt, a__U11(mark(x1), x2, x3))) MARK(plus(0, U11(x1, x2, x3))) -> c10(A__PLUS(0, a__U11(mark(x1), x2, x3))) MARK(plus(x0, U12(U11(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__U11(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U12(U12(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__U12(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U12(plus(z0, z1), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(x0)) MARK(plus(x0, U12(tt, x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U12(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U12(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U12(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U12(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U12(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(s(z0), U12(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(x0, U12(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U12(x1, x2, x3))) -> c10(A__PLUS(tt, a__U12(mark(x1), x2, x3))) MARK(plus(0, U12(x1, x2, x3))) -> c10(A__PLUS(0, a__U12(mark(x1), x2, x3))) MARK(plus(x0, plus(x1, U11(z0, z1, z2)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__U11(mark(z0), z1, z2))), MARK(x0)) MARK(plus(x0, plus(x1, U12(z0, z1, z2)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__U12(mark(z0), z1, z2))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(U11(z0, z1, z2), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__U11(mark(z0), z1, z2), mark(x2))), MARK(x0)) MARK(plus(x0, plus(U12(z0, z1, z2), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__U12(mark(z0), z1, z2), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c10(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c10(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c10(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(U11(z0, z1, z2), plus(x1, x2))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), plus(x1, x2))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c10(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))) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c10(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c10(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c10(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(U11(x0, x1, x2), s(z0))) -> c10(A__PLUS(a__U11(mark(x0), x1, x2), s(mark(z0))), MARK(U11(x0, x1, x2))) MARK(plus(U11(x0, x1, x2), 0)) -> c10(A__PLUS(a__U11(mark(x0), x1, x2), 0), MARK(U11(x0, x1, x2))) MARK(plus(U11(x0, z1, z2), x3)) -> c10(A__PLUS(U11(mark(x0), z1, z2), mark(x3)), MARK(U11(x0, z1, z2))) MARK(plus(U11(U11(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(plus(U11(U12(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(plus(U11(plus(z0, z1), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(U11(plus(z0, z1), x1, x2))) MARK(plus(U11(tt, x1, x2), x3)) -> c10(A__PLUS(a__U11(tt, x1, x2), mark(x3)), MARK(U11(tt, x1, x2))) MARK(plus(U11(s(z0), x1, x2), x3)) -> c10(A__PLUS(a__U11(s(mark(z0)), x1, x2), mark(x3)), MARK(U11(s(z0), x1, x2))) MARK(plus(U11(x0, x1, x2), tt)) -> c10(MARK(U11(x0, x1, x2))) MARK(plus(U11(0, x1, x2), x3)) -> c10(A__PLUS(a__U11(0, x1, x2), mark(x3))) MARK(plus(U12(x0, x1, x2), s(z0))) -> c10(A__PLUS(a__U12(mark(x0), x1, x2), s(mark(z0))), MARK(U12(x0, x1, x2))) MARK(plus(U12(x0, x1, x2), 0)) -> c10(A__PLUS(a__U12(mark(x0), x1, x2), 0), MARK(U12(x0, x1, x2))) MARK(plus(U12(x0, z1, z2), x3)) -> c10(A__PLUS(U12(mark(x0), z1, z2), mark(x3)), MARK(U12(x0, z1, z2))) MARK(plus(U12(U11(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(plus(U12(U12(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(plus(U12(plus(z0, z1), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(U12(plus(z0, z1), x1, x2))) MARK(plus(U12(tt, x1, x2), x3)) -> c10(A__PLUS(a__U12(tt, x1, x2), mark(x3)), MARK(U12(tt, x1, x2))) MARK(plus(U12(s(z0), x1, x2), x3)) -> c10(A__PLUS(a__U12(s(mark(z0)), x1, x2), mark(x3)), MARK(U12(s(z0), x1, x2))) MARK(plus(U12(x0, x1, x2), tt)) -> c10(MARK(U12(x0, x1, x2))) MARK(plus(U12(0, x1, x2), x3)) -> c10(A__PLUS(a__U12(0, x1, x2), mark(x3))) MARK(plus(plus(x0, x1), s(z0))) -> c10(A__PLUS(a__plus(mark(x0), mark(x1)), s(mark(z0))), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), 0)) -> c10(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c10(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, U11(z0, z1, z2)), x2)) -> c10(A__PLUS(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), mark(x2)), MARK(plus(x0, U11(z0, z1, z2)))) MARK(plus(plus(x0, U12(z0, z1, z2)), x2)) -> c10(A__PLUS(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), mark(x2)), MARK(plus(x0, U12(z0, z1, z2)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c10(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)) -> c10(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, s(z0)), x2)) -> c10(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(x0, 0), x2)) -> c10(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(U11(z0, z1, z2), x1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(plus(U11(z0, z1, z2), x1))) MARK(plus(plus(U12(z0, z1, z2), x1), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(plus(U12(z0, z1, z2), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c10(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)) -> c10(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(0, x1), x2)) -> c10(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(x0, x1), tt)) -> c10(MARK(plus(x0, x1))) MARK(plus(s(x0), s(z0))) -> c10(A__PLUS(s(mark(x0)), s(mark(z0))), MARK(s(x0))) MARK(plus(s(x0), 0)) -> c10(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(U11(z0, z1, z2)), x1)) -> c10(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x1)), MARK(s(U11(z0, z1, z2)))) MARK(plus(s(U12(z0, z1, z2)), x1)) -> c10(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x1)), MARK(s(U12(z0, z1, z2)))) MARK(plus(s(plus(z0, z1)), x1)) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c10(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(s(z0)), x1)) -> c10(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(0), x1)) -> c10(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(x0), x1)) -> c10(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c10(MARK(s(x0))) MARK(plus(tt, s(z0))) -> c10(A__PLUS(tt, s(mark(z0)))) MARK(plus(tt, 0)) -> c10(A__PLUS(tt, 0)) MARK(plus(0, s(z0))) -> c10(A__PLUS(0, s(mark(z0)))) MARK(plus(0, 0)) -> c10(A__PLUS(0, 0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_1, c9_1, c10_2, c10_1, c11_2, c11_1, c8_2, c9_2 ---------------------------------------- (201) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(x0, U11(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) by MARK(plus(x0, U11(x1, z1, z2))) -> c11(A__PLUS(mark(x0), U11(mark(x1), z1, z2)), MARK(U11(x1, z1, z2))) MARK(plus(x0, U11(U11(z0, z1, z2), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(a__U11(mark(z0), z1, z2), x2, x3)), MARK(U11(U11(z0, z1, z2), x2, x3))) MARK(plus(x0, U11(U12(z0, z1, z2), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(a__U12(mark(z0), z1, z2), x2, x3)), MARK(U11(U12(z0, z1, z2), x2, x3))) MARK(plus(x0, U11(plus(z0, z1), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(U11(plus(z0, z1), x2, x3))) MARK(plus(x0, U11(tt, x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(tt, x2, x3)), MARK(U11(tt, x2, x3))) MARK(plus(x0, U11(s(z0), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(s(mark(z0)), x2, x3)), MARK(U11(s(z0), x2, x3))) MARK(plus(x0, U11(0, x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(0, x2, x3)), MARK(U11(0, x2, x3))) MARK(plus(U11(z0, z1, z2), U11(x1, x2, x3))) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(U12(z0, z1, z2), U11(x1, x2, x3))) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(plus(z0, z1), U11(x1, x2, x3))) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(tt, U11(x1, x2, x3))) -> c11(A__PLUS(tt, a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(s(z0), U11(x1, x2, x3))) -> c11(A__PLUS(s(mark(z0)), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(0, U11(x1, x2, x3))) -> c11(A__PLUS(0, a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) ---------------------------------------- (202) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U12(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c3(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c3(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U12(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U12(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U12(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, 0) -> c3(A__PLUS(0, 0)) MARK(U11(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U11(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U11(U11(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U11(U11(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U11(U11(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U11(U11(x0, z1, z2), x3, x4)) -> c8(MARK(U11(x0, z1, z2))) MARK(U11(U11(0, x1, x2), x3, x4)) -> c8(A__U11(a__U11(0, x1, x2), x3, x4)) MARK(U11(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U11(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U11(U12(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U11(U12(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U11(U12(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U11(U12(x0, z1, z2), x3, x4)) -> c8(MARK(U12(x0, z1, z2))) MARK(U11(U12(0, x1, x2), x3, x4)) -> c8(A__U11(a__U12(0, x1, x2), x3, x4)) MARK(U11(plus(x0, U11(z0, z1, z2)), x2, x3)) -> 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x3))) -> c10(A__PLUS(mark(x0), a__U11(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U11(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U11(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(s(z0), U11(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(x0, U11(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U11(x1, x2, x3))) -> c10(A__PLUS(tt, a__U11(mark(x1), x2, x3))) MARK(plus(0, U11(x1, x2, x3))) -> c10(A__PLUS(0, a__U11(mark(x1), x2, x3))) MARK(plus(x0, U12(U11(z0, z1, z2), x2, 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c10(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(plus(U12(plus(z0, z1), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(U12(plus(z0, z1), x1, x2))) MARK(plus(U12(tt, x1, x2), x3)) -> c10(A__PLUS(a__U12(tt, x1, x2), mark(x3)), MARK(U12(tt, x1, x2))) MARK(plus(U12(s(z0), x1, x2), x3)) -> c10(A__PLUS(a__U12(s(mark(z0)), x1, x2), mark(x3)), MARK(U12(s(z0), x1, x2))) MARK(plus(U12(x0, x1, x2), tt)) -> c10(MARK(U12(x0, x1, x2))) MARK(plus(U12(0, x1, x2), x3)) -> c10(A__PLUS(a__U12(0, x1, x2), mark(x3))) MARK(plus(plus(x0, x1), s(z0))) -> c10(A__PLUS(a__plus(mark(x0), mark(x1)), s(mark(z0))), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), 0)) -> c10(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c10(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, U11(z0, z1, z2)), x2)) -> c10(A__PLUS(a__plus(mark(x0), a__U11(mark(z0), 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c10(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)) -> c10(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(0, x1), x2)) -> c10(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(x0, x1), tt)) -> c10(MARK(plus(x0, x1))) MARK(plus(s(x0), s(z0))) -> c10(A__PLUS(s(mark(x0)), s(mark(z0))), MARK(s(x0))) MARK(plus(s(x0), 0)) -> c10(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(U11(z0, z1, z2)), x1)) -> c10(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x1)), MARK(s(U11(z0, z1, z2)))) MARK(plus(s(U12(z0, z1, z2)), x1)) -> c10(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x1)), MARK(s(U12(z0, z1, z2)))) MARK(plus(s(plus(z0, z1)), x1)) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c10(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(s(z0)), x1)) -> c10(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(0), x1)) -> c10(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(x0), x1)) -> c10(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c10(MARK(s(x0))) MARK(plus(tt, s(z0))) -> c10(A__PLUS(tt, s(mark(z0)))) MARK(plus(tt, 0)) -> c10(A__PLUS(tt, 0)) MARK(plus(0, s(z0))) -> c10(A__PLUS(0, s(mark(z0)))) MARK(plus(0, 0)) -> c10(A__PLUS(0, 0)) MARK(plus(x0, U11(x1, z1, z2))) -> c11(A__PLUS(mark(x0), U11(mark(x1), z1, z2)), MARK(U11(x1, z1, z2))) MARK(plus(x0, U11(U11(z0, z1, z2), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(a__U11(mark(z0), z1, z2), x2, x3)), MARK(U11(U11(z0, z1, z2), x2, x3))) MARK(plus(x0, U11(U12(z0, z1, z2), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(a__U12(mark(z0), z1, z2), x2, x3)), MARK(U11(U12(z0, z1, z2), x2, x3))) MARK(plus(x0, U11(plus(z0, z1), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(U11(plus(z0, z1), x2, x3))) MARK(plus(x0, U11(tt, x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(tt, x2, x3)), MARK(U11(tt, x2, x3))) MARK(plus(x0, U11(s(z0), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(s(mark(z0)), x2, x3)), MARK(U11(s(z0), x2, x3))) MARK(plus(x0, U11(0, x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(0, x2, x3)), MARK(U11(0, x2, x3))) MARK(plus(U11(z0, z1, z2), U11(x1, x2, x3))) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(U12(z0, z1, z2), U11(x1, x2, x3))) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(plus(z0, z1), U11(x1, x2, x3))) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(tt, U11(x1, x2, x3))) -> c11(A__PLUS(tt, a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(s(z0), U11(x1, x2, x3))) -> c11(A__PLUS(s(mark(z0)), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(0, U11(x1, x2, x3))) -> c11(A__PLUS(0, a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, 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c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) 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MARK(U11(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U11(U11(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U11(U11(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U11(U11(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U11(U11(x0, z1, z2), x3, x4)) -> c8(MARK(U11(x0, z1, z2))) MARK(U11(U11(0, x1, x2), x3, x4)) -> c8(A__U11(a__U11(0, x1, x2), x3, x4)) MARK(U11(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U11(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U11(U12(plus(z0, z1), x1, x2), x3, x4)) -> 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MARK(U12(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U12(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U12(U11(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U12(U11(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U12(U11(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U12(U11(x0, z1, z2), x3, x4)) -> c9(MARK(U11(x0, z1, z2))) MARK(U12(U11(0, x1, x2), x3, x4)) -> c9(A__U12(a__U11(0, x1, x2), x3, x4)) MARK(U12(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U12(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> 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x3)) -> c9(A__U12(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U12(plus(x0, x1), x2, x3)) -> c9(MARK(plus(x0, x1))) MARK(plus(x0, U11(U11(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__U11(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U11(U12(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__U12(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U11(plus(z0, z1), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(tt, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U11(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U11(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(s(z0), U11(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(x0, U11(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U11(x1, x2, x3))) -> c10(A__PLUS(tt, a__U11(mark(x1), x2, x3))) MARK(plus(0, U11(x1, x2, x3))) -> c10(A__PLUS(0, a__U11(mark(x1), x2, x3))) MARK(plus(x0, U12(U11(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__U11(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U12(U12(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__U12(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U12(plus(z0, z1), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(x0)) MARK(plus(x0, U12(tt, x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U12(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U12(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U12(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U12(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U12(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(s(z0), U12(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(x0, U12(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U12(x1, x2, x3))) -> c10(A__PLUS(tt, a__U12(mark(x1), x2, x3))) MARK(plus(0, U12(x1, x2, x3))) -> c10(A__PLUS(0, a__U12(mark(x1), x2, x3))) MARK(plus(x0, plus(x1, U11(z0, z1, z2)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__U11(mark(z0), z1, z2))), MARK(x0)) MARK(plus(x0, plus(x1, U12(z0, z1, z2)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__U12(mark(z0), z1, z2))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(U11(z0, z1, z2), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__U11(mark(z0), z1, z2), mark(x2))), MARK(x0)) MARK(plus(x0, plus(U12(z0, z1, z2), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__U12(mark(z0), z1, z2), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c10(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c10(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c10(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(U11(z0, z1, z2), plus(x1, x2))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), plus(x1, x2))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c10(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))) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c10(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c10(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c10(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(U11(x0, x1, x2), s(z0))) -> c10(A__PLUS(a__U11(mark(x0), x1, x2), s(mark(z0))), MARK(U11(x0, x1, x2))) MARK(plus(U11(x0, x1, x2), 0)) -> c10(A__PLUS(a__U11(mark(x0), x1, x2), 0), MARK(U11(x0, x1, x2))) MARK(plus(U11(x0, z1, z2), x3)) -> c10(A__PLUS(U11(mark(x0), z1, z2), mark(x3)), MARK(U11(x0, z1, z2))) MARK(plus(U11(U11(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(plus(U11(U12(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(plus(U11(plus(z0, z1), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(U11(plus(z0, z1), x1, x2))) MARK(plus(U11(tt, x1, x2), x3)) -> c10(A__PLUS(a__U11(tt, x1, x2), mark(x3)), MARK(U11(tt, x1, x2))) MARK(plus(U11(s(z0), x1, x2), x3)) -> c10(A__PLUS(a__U11(s(mark(z0)), x1, x2), mark(x3)), MARK(U11(s(z0), x1, x2))) MARK(plus(U11(x0, x1, x2), tt)) -> c10(MARK(U11(x0, x1, x2))) MARK(plus(U11(0, x1, x2), x3)) -> c10(A__PLUS(a__U11(0, x1, x2), mark(x3))) MARK(plus(U12(x0, x1, x2), s(z0))) -> c10(A__PLUS(a__U12(mark(x0), x1, x2), s(mark(z0))), MARK(U12(x0, x1, x2))) MARK(plus(U12(x0, x1, x2), 0)) -> c10(A__PLUS(a__U12(mark(x0), x1, x2), 0), MARK(U12(x0, x1, x2))) MARK(plus(U12(x0, z1, z2), x3)) -> c10(A__PLUS(U12(mark(x0), z1, z2), mark(x3)), MARK(U12(x0, z1, z2))) MARK(plus(U12(U11(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(plus(U12(U12(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(plus(U12(plus(z0, z1), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(U12(plus(z0, z1), x1, x2))) MARK(plus(U12(tt, x1, x2), x3)) -> c10(A__PLUS(a__U12(tt, x1, x2), mark(x3)), MARK(U12(tt, x1, x2))) MARK(plus(U12(s(z0), x1, x2), x3)) -> c10(A__PLUS(a__U12(s(mark(z0)), x1, x2), mark(x3)), MARK(U12(s(z0), x1, x2))) MARK(plus(U12(x0, x1, x2), tt)) -> c10(MARK(U12(x0, x1, x2))) MARK(plus(U12(0, x1, x2), x3)) -> c10(A__PLUS(a__U12(0, x1, x2), mark(x3))) MARK(plus(plus(x0, x1), s(z0))) -> c10(A__PLUS(a__plus(mark(x0), mark(x1)), s(mark(z0))), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), 0)) -> c10(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c10(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, U11(z0, z1, z2)), x2)) -> c10(A__PLUS(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), mark(x2)), MARK(plus(x0, U11(z0, z1, z2)))) MARK(plus(plus(x0, U12(z0, z1, z2)), x2)) -> c10(A__PLUS(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), mark(x2)), MARK(plus(x0, U12(z0, z1, z2)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c10(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)) -> c10(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, s(z0)), x2)) -> c10(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(x0, 0), x2)) -> c10(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(U11(z0, z1, z2), x1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(plus(U11(z0, z1, z2), x1))) MARK(plus(plus(U12(z0, z1, z2), x1), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(plus(U12(z0, z1, z2), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c10(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)) -> c10(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(0, x1), x2)) -> c10(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(x0, x1), tt)) -> c10(MARK(plus(x0, x1))) MARK(plus(s(x0), s(z0))) -> c10(A__PLUS(s(mark(x0)), s(mark(z0))), MARK(s(x0))) MARK(plus(s(x0), 0)) -> c10(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(U11(z0, z1, z2)), x1)) -> c10(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x1)), MARK(s(U11(z0, z1, z2)))) MARK(plus(s(U12(z0, z1, z2)), x1)) -> c10(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x1)), MARK(s(U12(z0, z1, z2)))) MARK(plus(s(plus(z0, z1)), x1)) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c10(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(s(z0)), x1)) -> c10(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(0), x1)) -> c10(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(x0), x1)) -> c10(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c10(MARK(s(x0))) MARK(plus(tt, s(z0))) -> c10(A__PLUS(tt, s(mark(z0)))) MARK(plus(tt, 0)) -> c10(A__PLUS(tt, 0)) MARK(plus(0, s(z0))) -> c10(A__PLUS(0, s(mark(z0)))) MARK(plus(0, 0)) -> c10(A__PLUS(0, 0)) MARK(plus(x0, U11(x1, z1, z2))) -> c11(A__PLUS(mark(x0), U11(mark(x1), z1, z2)), MARK(U11(x1, z1, z2))) MARK(plus(x0, U11(U11(z0, z1, z2), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(a__U11(mark(z0), z1, z2), x2, x3)), MARK(U11(U11(z0, z1, z2), x2, x3))) MARK(plus(x0, U11(U12(z0, z1, z2), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(a__U12(mark(z0), z1, z2), x2, x3)), MARK(U11(U12(z0, z1, z2), x2, x3))) MARK(plus(x0, U11(plus(z0, z1), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(U11(plus(z0, z1), x2, x3))) MARK(plus(x0, U11(tt, x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(tt, x2, x3)), MARK(U11(tt, x2, x3))) MARK(plus(x0, U11(s(z0), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(s(mark(z0)), x2, x3)), MARK(U11(s(z0), x2, x3))) MARK(plus(x0, U11(0, x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(0, x2, x3)), MARK(U11(0, x2, x3))) MARK(plus(U11(z0, z1, z2), U11(x1, x2, x3))) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(U12(z0, z1, z2), U11(x1, x2, x3))) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(plus(z0, z1), U11(x1, x2, x3))) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(tt, U11(x1, x2, x3))) -> c11(A__PLUS(tt, a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(s(z0), U11(x1, x2, x3))) -> c11(A__PLUS(s(mark(z0)), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(0, U11(x1, x2, x3))) -> c11(A__PLUS(0, a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_1, c9_1, c10_2, c10_1, c11_2, c11_1, c8_2, c9_2 ---------------------------------------- (203) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (204) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U12(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c3(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c3(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U12(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U12(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U12(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, 0) -> c3(A__PLUS(0, 0)) MARK(U11(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U11(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U11(U11(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U11(U11(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U11(U11(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U11(U11(x0, z1, z2), x3, x4)) -> c8(MARK(U11(x0, z1, z2))) 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x1))) MARK(plus(plus(tt, x1), x2)) -> c10(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(0, x1), x2)) -> c10(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(x0, x1), tt)) -> c10(MARK(plus(x0, x1))) MARK(plus(s(x0), s(z0))) -> c10(A__PLUS(s(mark(x0)), s(mark(z0))), MARK(s(x0))) MARK(plus(s(x0), 0)) -> c10(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(U11(z0, z1, z2)), x1)) -> c10(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x1)), MARK(s(U11(z0, z1, z2)))) MARK(plus(s(U12(z0, z1, z2)), x1)) -> c10(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x1)), MARK(s(U12(z0, z1, z2)))) MARK(plus(s(plus(z0, z1)), x1)) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c10(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(s(z0)), x1)) -> c10(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(0), x1)) -> c10(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(x0), x1)) -> c10(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c10(MARK(s(x0))) MARK(plus(tt, s(z0))) -> c10(A__PLUS(tt, s(mark(z0)))) MARK(plus(tt, 0)) -> c10(A__PLUS(tt, 0)) MARK(plus(0, s(z0))) -> c10(A__PLUS(0, s(mark(z0)))) MARK(plus(0, 0)) -> c10(A__PLUS(0, 0)) MARK(plus(x0, U11(U11(z0, z1, z2), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(a__U11(mark(z0), z1, z2), x2, x3)), MARK(U11(U11(z0, z1, z2), x2, x3))) MARK(plus(x0, U11(U12(z0, z1, z2), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(a__U12(mark(z0), z1, z2), x2, x3)), MARK(U11(U12(z0, z1, z2), x2, x3))) MARK(plus(x0, U11(plus(z0, z1), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(U11(plus(z0, z1), x2, x3))) MARK(plus(x0, U11(tt, x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(tt, x2, x3)), MARK(U11(tt, x2, x3))) MARK(plus(x0, U11(s(z0), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(s(mark(z0)), x2, x3)), MARK(U11(s(z0), x2, x3))) MARK(plus(U11(z0, z1, z2), U11(x1, x2, x3))) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(U12(z0, z1, z2), U11(x1, x2, x3))) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(plus(z0, z1), U11(x1, x2, x3))) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(tt, U11(x1, x2, x3))) -> c11(A__PLUS(tt, a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(s(z0), U11(x1, x2, x3))) -> c11(A__PLUS(s(mark(z0)), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(0, U11(x1, x2, x3))) -> c11(A__PLUS(0, a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(x0, U11(x1, z1, z2))) -> c11(MARK(U11(x1, z1, z2))) MARK(plus(x0, U11(0, x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(0, x2, x3))) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, 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x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> 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A__U12(tt, x0, s(U11(z0, z1, z2))) -> c3(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c3(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U12(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U12(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U12(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, 0) -> c3(A__PLUS(0, 0)) MARK(U11(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U11(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U11(U11(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U11(U11(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U11(U11(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U11(U11(x0, z1, z2), x3, x4)) -> c8(MARK(U11(x0, z1, z2))) MARK(U11(U11(0, x1, x2), x3, x4)) -> c8(A__U11(a__U11(0, x1, x2), x3, x4)) MARK(U11(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U11(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U11(U12(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U11(U12(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U11(U12(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U11(U12(x0, z1, z2), x3, x4)) -> c8(MARK(U12(x0, z1, z2))) MARK(U11(U12(0, x1, x2), x3, x4)) -> c8(A__U11(a__U12(0, x1, x2), x3, x4)) MARK(U11(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U11(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U11(plus(x0, plus(z0, z1)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U11(plus(x0, tt), x2, x3)) -> c8(A__U11(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U11(plus(x0, s(z0)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U11(plus(x0, 0), x2, x3)) -> c8(A__U11(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U11(plus(U11(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U11(plus(U12(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U11(plus(plus(z0, z1), x1), x2, x3)) -> c8(A__U11(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U11(plus(tt, x1), x2, x3)) -> c8(A__U11(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U11(plus(s(z0), x1), x2, x3)) -> c8(A__U11(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U11(plus(0, x1), x2, x3)) -> c8(A__U11(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U11(plus(x0, x1), x2, x3)) -> c8(MARK(plus(x0, x1))) MARK(U12(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U12(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U12(U11(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U12(U11(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U12(U11(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U12(U11(x0, z1, z2), x3, x4)) -> c9(MARK(U11(x0, z1, z2))) MARK(U12(U11(0, x1, x2), x3, x4)) -> c9(A__U12(a__U11(0, x1, x2), x3, x4)) MARK(U12(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U12(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U12(U12(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U12(U12(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U12(U12(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U12(U12(x0, z1, z2), x3, x4)) -> c9(MARK(U12(x0, z1, z2))) MARK(U12(U12(0, x1, x2), x3, x4)) -> c9(A__U12(a__U12(0, x1, x2), x3, x4)) MARK(U12(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U12(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U12(plus(x0, plus(z0, z1)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U12(plus(x0, tt), x2, x3)) -> c9(A__U12(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U12(plus(x0, s(z0)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U12(plus(x0, 0), x2, x3)) -> c9(A__U12(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U12(plus(U11(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U12(plus(U12(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U12(plus(plus(z0, z1), x1), x2, x3)) -> c9(A__U12(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U12(plus(tt, x1), x2, x3)) -> c9(A__U12(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U12(plus(s(z0), x1), x2, x3)) -> c9(A__U12(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U12(plus(0, x1), x2, x3)) -> c9(A__U12(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U12(plus(x0, x1), x2, x3)) -> c9(MARK(plus(x0, x1))) MARK(plus(x0, U11(U11(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__U11(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U11(U12(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__U12(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U11(plus(z0, z1), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(tt, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U11(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U11(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(s(z0), U11(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(x0, U11(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U11(x1, x2, x3))) -> c10(A__PLUS(tt, a__U11(mark(x1), x2, x3))) MARK(plus(0, U11(x1, x2, x3))) -> c10(A__PLUS(0, a__U11(mark(x1), x2, x3))) MARK(plus(x0, U12(U11(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__U11(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U12(U12(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__U12(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U12(plus(z0, z1), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(x0)) MARK(plus(x0, U12(tt, x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U12(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U12(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U12(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U12(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U12(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(s(z0), U12(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(x0, U12(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U12(x1, x2, x3))) -> c10(A__PLUS(tt, a__U12(mark(x1), x2, x3))) MARK(plus(0, U12(x1, x2, x3))) -> c10(A__PLUS(0, a__U12(mark(x1), x2, x3))) MARK(plus(x0, plus(x1, U11(z0, z1, z2)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__U11(mark(z0), z1, z2))), MARK(x0)) MARK(plus(x0, plus(x1, U12(z0, z1, z2)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__U12(mark(z0), z1, z2))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(U11(z0, z1, z2), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__U11(mark(z0), z1, z2), mark(x2))), MARK(x0)) MARK(plus(x0, plus(U12(z0, z1, z2), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__U12(mark(z0), z1, z2), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c10(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c10(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c10(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(U11(z0, z1, z2), plus(x1, x2))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), plus(x1, x2))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c10(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))) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c10(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c10(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c10(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(U11(x0, x1, x2), s(z0))) -> c10(A__PLUS(a__U11(mark(x0), x1, x2), s(mark(z0))), MARK(U11(x0, x1, x2))) MARK(plus(U11(x0, x1, x2), 0)) -> c10(A__PLUS(a__U11(mark(x0), x1, x2), 0), MARK(U11(x0, x1, x2))) MARK(plus(U11(x0, z1, z2), x3)) -> c10(A__PLUS(U11(mark(x0), z1, z2), mark(x3)), MARK(U11(x0, z1, z2))) MARK(plus(U11(U11(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(plus(U11(U12(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(plus(U11(plus(z0, z1), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(U11(plus(z0, z1), x1, x2))) MARK(plus(U11(tt, x1, x2), x3)) -> c10(A__PLUS(a__U11(tt, x1, x2), mark(x3)), MARK(U11(tt, x1, x2))) MARK(plus(U11(s(z0), x1, x2), x3)) -> c10(A__PLUS(a__U11(s(mark(z0)), x1, x2), mark(x3)), MARK(U11(s(z0), x1, x2))) MARK(plus(U11(x0, x1, x2), tt)) -> c10(MARK(U11(x0, x1, x2))) MARK(plus(U11(0, x1, x2), x3)) -> c10(A__PLUS(a__U11(0, x1, x2), mark(x3))) MARK(plus(U12(x0, x1, x2), s(z0))) -> c10(A__PLUS(a__U12(mark(x0), x1, x2), s(mark(z0))), MARK(U12(x0, x1, x2))) MARK(plus(U12(x0, x1, x2), 0)) -> c10(A__PLUS(a__U12(mark(x0), x1, x2), 0), MARK(U12(x0, x1, x2))) MARK(plus(U12(x0, z1, z2), x3)) -> c10(A__PLUS(U12(mark(x0), z1, z2), mark(x3)), MARK(U12(x0, z1, z2))) MARK(plus(U12(U11(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(plus(U12(U12(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(plus(U12(plus(z0, z1), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(U12(plus(z0, z1), x1, x2))) MARK(plus(U12(tt, x1, x2), x3)) -> c10(A__PLUS(a__U12(tt, x1, x2), mark(x3)), MARK(U12(tt, x1, x2))) MARK(plus(U12(s(z0), x1, x2), x3)) -> c10(A__PLUS(a__U12(s(mark(z0)), x1, x2), mark(x3)), MARK(U12(s(z0), x1, x2))) MARK(plus(U12(x0, x1, x2), tt)) -> c10(MARK(U12(x0, x1, x2))) MARK(plus(U12(0, x1, x2), x3)) -> c10(A__PLUS(a__U12(0, x1, x2), mark(x3))) MARK(plus(plus(x0, x1), s(z0))) -> c10(A__PLUS(a__plus(mark(x0), mark(x1)), s(mark(z0))), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), 0)) -> c10(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c10(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, U11(z0, z1, z2)), x2)) -> c10(A__PLUS(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), mark(x2)), MARK(plus(x0, U11(z0, z1, z2)))) MARK(plus(plus(x0, U12(z0, z1, z2)), x2)) -> c10(A__PLUS(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), mark(x2)), MARK(plus(x0, U12(z0, z1, z2)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c10(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)) -> c10(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, s(z0)), x2)) -> c10(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(x0, 0), x2)) -> c10(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(U11(z0, z1, z2), x1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(plus(U11(z0, z1, z2), x1))) MARK(plus(plus(U12(z0, z1, z2), x1), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(plus(U12(z0, z1, z2), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c10(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)) -> c10(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(0, x1), x2)) -> c10(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(x0, x1), tt)) -> c10(MARK(plus(x0, x1))) MARK(plus(s(x0), s(z0))) -> c10(A__PLUS(s(mark(x0)), s(mark(z0))), MARK(s(x0))) MARK(plus(s(x0), 0)) -> c10(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(U11(z0, z1, z2)), x1)) -> c10(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x1)), MARK(s(U11(z0, z1, z2)))) MARK(plus(s(U12(z0, z1, z2)), x1)) -> c10(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x1)), MARK(s(U12(z0, z1, z2)))) MARK(plus(s(plus(z0, z1)), x1)) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c10(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(s(z0)), x1)) -> c10(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(0), x1)) -> c10(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(x0), x1)) -> c10(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c10(MARK(s(x0))) MARK(plus(tt, s(z0))) -> c10(A__PLUS(tt, s(mark(z0)))) MARK(plus(tt, 0)) -> c10(A__PLUS(tt, 0)) MARK(plus(0, s(z0))) -> c10(A__PLUS(0, s(mark(z0)))) MARK(plus(0, 0)) -> c10(A__PLUS(0, 0)) MARK(plus(x0, U11(U11(z0, z1, z2), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(a__U11(mark(z0), z1, z2), x2, x3)), MARK(U11(U11(z0, z1, z2), x2, x3))) MARK(plus(x0, U11(U12(z0, z1, z2), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(a__U12(mark(z0), z1, z2), x2, x3)), MARK(U11(U12(z0, z1, z2), x2, x3))) MARK(plus(x0, U11(plus(z0, z1), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(U11(plus(z0, z1), x2, x3))) MARK(plus(x0, U11(tt, x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(tt, x2, x3)), MARK(U11(tt, x2, x3))) MARK(plus(x0, U11(s(z0), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(s(mark(z0)), x2, x3)), MARK(U11(s(z0), x2, x3))) MARK(plus(U11(z0, z1, z2), U11(x1, x2, x3))) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(U12(z0, z1, z2), U11(x1, x2, x3))) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(plus(z0, z1), U11(x1, x2, x3))) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(tt, U11(x1, x2, x3))) -> c11(A__PLUS(tt, a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(s(z0), U11(x1, x2, x3))) -> c11(A__PLUS(s(mark(z0)), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(0, U11(x1, x2, x3))) -> c11(A__PLUS(0, a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(x0, U11(x1, z1, z2))) -> c11(MARK(U11(x1, z1, z2))) MARK(plus(x0, U11(0, x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(0, x2, x3))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_1, c9_1, c10_2, c10_1, c11_2, c11_1, c8_2, c9_2 ---------------------------------------- (205) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(x0, U12(z0, z1, z2))) -> c11(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) by MARK(plus(x0, U12(x1, z1, z2))) -> c11(A__PLUS(mark(x0), U12(mark(x1), z1, z2)), MARK(U12(x1, z1, z2))) MARK(plus(x0, U12(U11(z0, z1, z2), x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(a__U11(mark(z0), z1, z2), x2, x3)), MARK(U12(U11(z0, z1, z2), x2, x3))) MARK(plus(x0, U12(U12(z0, z1, z2), x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(a__U12(mark(z0), z1, z2), x2, x3)), MARK(U12(U12(z0, z1, z2), x2, x3))) MARK(plus(x0, U12(plus(z0, z1), x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(U12(plus(z0, z1), x2, x3))) MARK(plus(x0, U12(tt, x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(tt, x2, x3)), MARK(U12(tt, x2, x3))) MARK(plus(x0, U12(s(z0), x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(s(mark(z0)), x2, x3)), MARK(U12(s(z0), x2, x3))) MARK(plus(x0, U12(0, x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(0, x2, x3)), MARK(U12(0, x2, x3))) MARK(plus(U11(z0, z1, z2), U12(x1, x2, x3))) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(U12(z0, z1, z2), U12(x1, x2, x3))) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(plus(z0, z1), U12(x1, x2, x3))) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(tt, U12(x1, x2, x3))) -> c11(A__PLUS(tt, a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(s(z0), U12(x1, x2, x3))) -> c11(A__PLUS(s(mark(z0)), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(0, U12(x1, x2, x3))) -> c11(A__PLUS(0, a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) ---------------------------------------- (206) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, 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z2), x2, x3)), MARK(U11(U12(z0, z1, z2), x2, x3))) MARK(plus(x0, U11(plus(z0, z1), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(U11(plus(z0, z1), x2, x3))) MARK(plus(x0, U11(tt, x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(tt, x2, x3)), MARK(U11(tt, x2, x3))) MARK(plus(x0, U11(s(z0), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(s(mark(z0)), x2, x3)), MARK(U11(s(z0), x2, x3))) MARK(plus(U11(z0, z1, z2), U11(x1, x2, x3))) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(U12(z0, z1, z2), U11(x1, x2, x3))) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(plus(z0, z1), U11(x1, x2, x3))) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(tt, U11(x1, x2, x3))) -> c11(A__PLUS(tt, a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(s(z0), U11(x1, x2, x3))) -> c11(A__PLUS(s(mark(z0)), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(0, U11(x1, x2, x3))) -> c11(A__PLUS(0, a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(x0, U11(x1, z1, z2))) -> c11(MARK(U11(x1, z1, z2))) MARK(plus(x0, U11(0, x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(0, x2, x3))) MARK(plus(x0, U12(x1, z1, z2))) -> c11(A__PLUS(mark(x0), U12(mark(x1), z1, z2)), MARK(U12(x1, z1, z2))) MARK(plus(x0, U12(U11(z0, z1, z2), x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(a__U11(mark(z0), z1, z2), x2, x3)), MARK(U12(U11(z0, z1, z2), x2, x3))) MARK(plus(x0, U12(U12(z0, z1, z2), x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(a__U12(mark(z0), z1, z2), x2, x3)), MARK(U12(U12(z0, z1, z2), x2, x3))) MARK(plus(x0, U12(plus(z0, z1), x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(U12(plus(z0, z1), x2, x3))) MARK(plus(x0, U12(tt, x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(tt, x2, x3)), MARK(U12(tt, x2, x3))) MARK(plus(x0, U12(s(z0), x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(s(mark(z0)), x2, x3)), MARK(U12(s(z0), x2, x3))) MARK(plus(x0, U12(0, x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(0, x2, x3)), MARK(U12(0, x2, x3))) MARK(plus(U11(z0, z1, z2), U12(x1, x2, x3))) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(U12(z0, z1, z2), U12(x1, x2, x3))) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(plus(z0, z1), U12(x1, x2, x3))) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(tt, U12(x1, x2, x3))) -> c11(A__PLUS(tt, a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(s(z0), U12(x1, x2, x3))) -> c11(A__PLUS(s(mark(z0)), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(0, U12(x1, x2, x3))) -> c11(A__PLUS(0, a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> 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c10(MARK(x0)) MARK(plus(tt, U11(x1, x2, x3))) -> c10(A__PLUS(tt, a__U11(mark(x1), x2, x3))) MARK(plus(0, U11(x1, x2, x3))) -> c10(A__PLUS(0, a__U11(mark(x1), x2, x3))) MARK(plus(x0, U12(U11(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__U11(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U12(U12(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__U12(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U12(plus(z0, z1), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(x0)) MARK(plus(x0, U12(tt, x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U12(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U12(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U12(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U12(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U12(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(s(z0), U12(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(x0, U12(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U12(x1, x2, x3))) -> c10(A__PLUS(tt, a__U12(mark(x1), x2, x3))) MARK(plus(0, U12(x1, x2, x3))) -> c10(A__PLUS(0, a__U12(mark(x1), x2, x3))) MARK(plus(x0, plus(x1, U11(z0, z1, z2)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__U11(mark(z0), z1, z2))), MARK(x0)) MARK(plus(x0, plus(x1, U12(z0, z1, z2)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__U12(mark(z0), z1, z2))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(U11(z0, z1, z2), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__U11(mark(z0), z1, z2), mark(x2))), MARK(x0)) MARK(plus(x0, plus(U12(z0, z1, z2), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__U12(mark(z0), z1, z2), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c10(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c10(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c10(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(U11(z0, z1, z2), plus(x1, x2))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), plus(x1, x2))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c10(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))) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c10(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c10(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c10(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(U11(x0, x1, x2), s(z0))) -> c10(A__PLUS(a__U11(mark(x0), x1, x2), s(mark(z0))), MARK(U11(x0, x1, x2))) MARK(plus(U11(x0, x1, x2), 0)) -> c10(A__PLUS(a__U11(mark(x0), x1, x2), 0), MARK(U11(x0, x1, x2))) MARK(plus(U11(x0, z1, z2), x3)) -> c10(A__PLUS(U11(mark(x0), z1, z2), mark(x3)), MARK(U11(x0, z1, z2))) MARK(plus(U11(U11(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(plus(U11(U12(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(plus(U11(plus(z0, z1), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(U11(plus(z0, z1), x1, x2))) MARK(plus(U11(tt, x1, x2), x3)) -> c10(A__PLUS(a__U11(tt, x1, x2), mark(x3)), MARK(U11(tt, x1, x2))) MARK(plus(U11(s(z0), x1, x2), x3)) -> c10(A__PLUS(a__U11(s(mark(z0)), x1, x2), mark(x3)), MARK(U11(s(z0), x1, x2))) MARK(plus(U11(x0, x1, x2), tt)) -> c10(MARK(U11(x0, x1, x2))) MARK(plus(U11(0, x1, x2), x3)) -> c10(A__PLUS(a__U11(0, x1, x2), mark(x3))) MARK(plus(U12(x0, x1, x2), s(z0))) -> c10(A__PLUS(a__U12(mark(x0), x1, x2), s(mark(z0))), MARK(U12(x0, x1, x2))) MARK(plus(U12(x0, x1, x2), 0)) -> c10(A__PLUS(a__U12(mark(x0), x1, x2), 0), MARK(U12(x0, x1, x2))) MARK(plus(U12(x0, z1, z2), x3)) -> c10(A__PLUS(U12(mark(x0), z1, z2), mark(x3)), MARK(U12(x0, z1, z2))) MARK(plus(U12(U11(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(plus(U12(U12(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(plus(U12(plus(z0, z1), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(U12(plus(z0, z1), x1, x2))) MARK(plus(U12(tt, x1, x2), x3)) -> c10(A__PLUS(a__U12(tt, x1, x2), mark(x3)), MARK(U12(tt, x1, x2))) MARK(plus(U12(s(z0), x1, x2), x3)) -> c10(A__PLUS(a__U12(s(mark(z0)), x1, x2), mark(x3)), MARK(U12(s(z0), x1, x2))) MARK(plus(U12(x0, x1, x2), tt)) -> c10(MARK(U12(x0, x1, x2))) MARK(plus(U12(0, x1, x2), x3)) -> c10(A__PLUS(a__U12(0, x1, x2), mark(x3))) MARK(plus(plus(x0, x1), s(z0))) -> c10(A__PLUS(a__plus(mark(x0), mark(x1)), s(mark(z0))), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), 0)) -> c10(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c10(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, U11(z0, z1, z2)), x2)) -> c10(A__PLUS(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), mark(x2)), MARK(plus(x0, U11(z0, z1, z2)))) MARK(plus(plus(x0, U12(z0, z1, z2)), x2)) -> c10(A__PLUS(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), mark(x2)), MARK(plus(x0, U12(z0, z1, z2)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c10(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)) -> c10(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, s(z0)), x2)) -> c10(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(x0, 0), x2)) -> c10(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(U11(z0, z1, z2), x1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(plus(U11(z0, z1, z2), x1))) MARK(plus(plus(U12(z0, z1, z2), x1), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(plus(U12(z0, z1, z2), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c10(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)) -> c10(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(0, x1), x2)) -> c10(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(x0, x1), tt)) -> c10(MARK(plus(x0, x1))) MARK(plus(s(x0), s(z0))) -> c10(A__PLUS(s(mark(x0)), s(mark(z0))), MARK(s(x0))) MARK(plus(s(x0), 0)) -> c10(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(U11(z0, z1, z2)), x1)) -> c10(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x1)), MARK(s(U11(z0, z1, z2)))) MARK(plus(s(U12(z0, z1, z2)), x1)) -> c10(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x1)), MARK(s(U12(z0, z1, z2)))) MARK(plus(s(plus(z0, z1)), x1)) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c10(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(s(z0)), x1)) -> c10(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(0), x1)) -> c10(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(x0), x1)) -> c10(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c10(MARK(s(x0))) MARK(plus(tt, s(z0))) -> c10(A__PLUS(tt, s(mark(z0)))) MARK(plus(tt, 0)) -> c10(A__PLUS(tt, 0)) MARK(plus(0, s(z0))) -> c10(A__PLUS(0, s(mark(z0)))) MARK(plus(0, 0)) -> c10(A__PLUS(0, 0)) MARK(plus(x0, U11(U11(z0, z1, z2), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(a__U11(mark(z0), z1, z2), x2, x3)), MARK(U11(U11(z0, z1, z2), x2, x3))) MARK(plus(x0, U11(U12(z0, z1, z2), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(a__U12(mark(z0), z1, z2), x2, x3)), MARK(U11(U12(z0, z1, z2), x2, x3))) MARK(plus(x0, U11(plus(z0, z1), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(U11(plus(z0, z1), x2, x3))) MARK(plus(x0, U11(tt, x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(tt, x2, x3)), MARK(U11(tt, x2, x3))) MARK(plus(x0, U11(s(z0), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(s(mark(z0)), x2, x3)), MARK(U11(s(z0), x2, x3))) MARK(plus(U11(z0, z1, z2), U11(x1, x2, x3))) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(U12(z0, z1, z2), U11(x1, x2, x3))) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(plus(z0, z1), U11(x1, x2, x3))) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(tt, U11(x1, x2, x3))) -> c11(A__PLUS(tt, a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(s(z0), U11(x1, x2, x3))) -> c11(A__PLUS(s(mark(z0)), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(0, U11(x1, x2, x3))) -> c11(A__PLUS(0, a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(x0, U11(x1, z1, z2))) -> c11(MARK(U11(x1, z1, z2))) MARK(plus(x0, U11(0, x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(0, x2, x3))) MARK(plus(x0, U12(x1, z1, z2))) -> c11(A__PLUS(mark(x0), U12(mark(x1), z1, z2)), MARK(U12(x1, z1, z2))) MARK(plus(x0, U12(U11(z0, z1, z2), x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(a__U11(mark(z0), z1, z2), x2, x3)), MARK(U12(U11(z0, z1, z2), x2, x3))) MARK(plus(x0, U12(U12(z0, z1, z2), x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(a__U12(mark(z0), z1, z2), x2, x3)), MARK(U12(U12(z0, z1, z2), x2, x3))) MARK(plus(x0, U12(plus(z0, z1), x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(U12(plus(z0, z1), x2, x3))) MARK(plus(x0, U12(tt, x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(tt, x2, x3)), MARK(U12(tt, x2, x3))) MARK(plus(x0, U12(s(z0), x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(s(mark(z0)), x2, x3)), MARK(U12(s(z0), x2, x3))) MARK(plus(x0, U12(0, x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(0, x2, x3)), MARK(U12(0, x2, x3))) MARK(plus(U11(z0, z1, z2), U12(x1, x2, x3))) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(U12(z0, z1, z2), U12(x1, x2, x3))) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(plus(z0, z1), U12(x1, x2, x3))) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(tt, U12(x1, x2, x3))) -> c11(A__PLUS(tt, a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(s(z0), U12(x1, x2, x3))) -> c11(A__PLUS(s(mark(z0)), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(0, U12(x1, x2, x3))) -> c11(A__PLUS(0, a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_1, c9_1, c10_2, c10_1, c11_2, c11_1, c8_2, c9_2 ---------------------------------------- (207) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (208) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U12(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c3(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c3(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U12(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U12(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U12(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, 0) -> c3(A__PLUS(0, 0)) MARK(U11(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U11(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U11(U11(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U11(U11(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U11(U11(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U11(U11(x0, z1, z2), x3, x4)) -> c8(MARK(U11(x0, z1, z2))) MARK(U11(U11(0, x1, x2), x3, x4)) -> c8(A__U11(a__U11(0, x1, x2), x3, x4)) MARK(U11(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U11(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U11(U12(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U11(U12(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U11(U12(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U11(U12(x0, z1, z2), x3, x4)) -> c8(MARK(U12(x0, z1, z2))) MARK(U11(U12(0, x1, x2), x3, x4)) -> c8(A__U11(a__U12(0, x1, x2), x3, x4)) MARK(U11(plus(x0, U11(z0, z1, z2)), x2, x3)) -> 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c10(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)) -> c10(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(0, x1), x2)) -> c10(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(x0, x1), tt)) -> c10(MARK(plus(x0, x1))) MARK(plus(s(x0), s(z0))) -> c10(A__PLUS(s(mark(x0)), s(mark(z0))), MARK(s(x0))) MARK(plus(s(x0), 0)) -> c10(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(U11(z0, z1, z2)), x1)) -> c10(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x1)), MARK(s(U11(z0, z1, z2)))) MARK(plus(s(U12(z0, z1, z2)), x1)) -> c10(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x1)), MARK(s(U12(z0, z1, z2)))) MARK(plus(s(plus(z0, z1)), x1)) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c10(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(s(z0)), x1)) -> c10(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(0), x1)) -> c10(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(x0), x1)) -> c10(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c10(MARK(s(x0))) MARK(plus(tt, s(z0))) -> c10(A__PLUS(tt, s(mark(z0)))) MARK(plus(tt, 0)) -> c10(A__PLUS(tt, 0)) MARK(plus(0, s(z0))) -> c10(A__PLUS(0, s(mark(z0)))) MARK(plus(0, 0)) -> c10(A__PLUS(0, 0)) MARK(plus(x0, U11(U11(z0, z1, z2), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(a__U11(mark(z0), z1, z2), x2, x3)), MARK(U11(U11(z0, z1, z2), x2, x3))) MARK(plus(x0, U11(U12(z0, z1, z2), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(a__U12(mark(z0), z1, z2), x2, x3)), MARK(U11(U12(z0, z1, z2), x2, x3))) MARK(plus(x0, U11(plus(z0, z1), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(U11(plus(z0, z1), x2, x3))) MARK(plus(x0, U11(tt, x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(tt, x2, x3)), MARK(U11(tt, x2, x3))) MARK(plus(x0, U11(s(z0), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(s(mark(z0)), x2, x3)), MARK(U11(s(z0), x2, x3))) MARK(plus(U11(z0, z1, z2), U11(x1, x2, x3))) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(U12(z0, z1, z2), U11(x1, x2, x3))) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(plus(z0, z1), U11(x1, x2, x3))) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(tt, U11(x1, x2, x3))) -> c11(A__PLUS(tt, a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(s(z0), U11(x1, x2, x3))) -> c11(A__PLUS(s(mark(z0)), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(0, U11(x1, x2, x3))) -> c11(A__PLUS(0, a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(x0, U11(x1, z1, z2))) -> c11(MARK(U11(x1, z1, z2))) MARK(plus(x0, U11(0, x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(0, x2, x3))) MARK(plus(x0, U12(U11(z0, z1, z2), x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(a__U11(mark(z0), z1, z2), x2, x3)), MARK(U12(U11(z0, z1, z2), x2, x3))) MARK(plus(x0, U12(U12(z0, z1, z2), x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(a__U12(mark(z0), z1, z2), x2, x3)), MARK(U12(U12(z0, z1, z2), x2, x3))) MARK(plus(x0, U12(plus(z0, z1), x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(U12(plus(z0, z1), x2, x3))) MARK(plus(x0, U12(tt, x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(tt, x2, x3)), MARK(U12(tt, x2, x3))) MARK(plus(x0, U12(s(z0), x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(s(mark(z0)), x2, x3)), MARK(U12(s(z0), x2, x3))) MARK(plus(U11(z0, z1, z2), U12(x1, x2, x3))) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(U12(z0, z1, z2), U12(x1, x2, x3))) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(plus(z0, z1), U12(x1, x2, x3))) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(tt, U12(x1, x2, x3))) -> c11(A__PLUS(tt, a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(s(z0), U12(x1, x2, x3))) -> c11(A__PLUS(s(mark(z0)), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(0, U12(x1, x2, x3))) -> c11(A__PLUS(0, a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(x0, U12(x1, z1, z2))) -> c11(MARK(U12(x1, z1, z2))) MARK(plus(x0, U12(0, x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(0, x2, x3))) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U12(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c3(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c3(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U12(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U12(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U12(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, 0) -> c3(A__PLUS(0, 0)) MARK(U11(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U11(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U11(U11(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U11(U11(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U11(U11(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U11(U11(x0, z1, z2), x3, x4)) -> c8(MARK(U11(x0, z1, z2))) MARK(U11(U11(0, x1, x2), x3, x4)) -> c8(A__U11(a__U11(0, x1, x2), x3, x4)) MARK(U11(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U11(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U11(U12(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U11(U12(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U11(U12(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U11(U12(x0, z1, z2), x3, x4)) -> c8(MARK(U12(x0, z1, z2))) MARK(U11(U12(0, x1, x2), x3, x4)) -> c8(A__U11(a__U12(0, x1, x2), x3, x4)) MARK(U11(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U11(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U11(plus(x0, plus(z0, z1)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U11(plus(x0, tt), x2, x3)) -> c8(A__U11(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U11(plus(x0, s(z0)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U11(plus(x0, 0), x2, x3)) -> c8(A__U11(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U11(plus(U11(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U11(plus(U12(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U11(plus(plus(z0, z1), x1), x2, x3)) -> c8(A__U11(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U11(plus(tt, x1), x2, x3)) -> c8(A__U11(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U11(plus(s(z0), x1), x2, x3)) -> c8(A__U11(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U11(plus(0, x1), x2, x3)) -> c8(A__U11(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U11(plus(x0, x1), x2, x3)) -> c8(MARK(plus(x0, x1))) MARK(U12(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U12(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U12(U11(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U12(U11(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U12(U11(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U12(U11(x0, z1, z2), x3, x4)) -> c9(MARK(U11(x0, z1, z2))) MARK(U12(U11(0, x1, x2), x3, x4)) -> c9(A__U12(a__U11(0, x1, x2), x3, x4)) MARK(U12(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U12(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U12(U12(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U12(U12(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U12(U12(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U12(U12(x0, z1, z2), x3, x4)) -> c9(MARK(U12(x0, z1, z2))) MARK(U12(U12(0, x1, x2), x3, x4)) -> c9(A__U12(a__U12(0, x1, x2), x3, x4)) MARK(U12(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U12(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U12(plus(x0, plus(z0, z1)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U12(plus(x0, tt), x2, x3)) -> c9(A__U12(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U12(plus(x0, s(z0)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U12(plus(x0, 0), x2, x3)) -> c9(A__U12(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U12(plus(U11(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U12(plus(U12(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U12(plus(plus(z0, z1), x1), x2, x3)) -> c9(A__U12(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U12(plus(tt, x1), x2, x3)) -> c9(A__U12(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U12(plus(s(z0), x1), x2, x3)) -> c9(A__U12(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U12(plus(0, x1), x2, x3)) -> c9(A__U12(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U12(plus(x0, x1), x2, x3)) -> c9(MARK(plus(x0, x1))) MARK(plus(x0, U11(U11(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__U11(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U11(U12(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__U12(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U11(plus(z0, z1), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(tt, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U11(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U11(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(s(z0), U11(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(x0, U11(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U11(x1, x2, x3))) -> c10(A__PLUS(tt, a__U11(mark(x1), x2, x3))) MARK(plus(0, U11(x1, x2, x3))) -> c10(A__PLUS(0, a__U11(mark(x1), x2, x3))) MARK(plus(x0, U12(U11(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__U11(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U12(U12(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__U12(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U12(plus(z0, z1), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(x0)) MARK(plus(x0, U12(tt, x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U12(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U12(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U12(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U12(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U12(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(s(z0), U12(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(x0, U12(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U12(x1, x2, x3))) -> c10(A__PLUS(tt, a__U12(mark(x1), x2, x3))) MARK(plus(0, U12(x1, x2, x3))) -> c10(A__PLUS(0, a__U12(mark(x1), x2, x3))) MARK(plus(x0, plus(x1, U11(z0, z1, z2)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__U11(mark(z0), z1, z2))), MARK(x0)) MARK(plus(x0, plus(x1, U12(z0, z1, z2)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__U12(mark(z0), z1, z2))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(U11(z0, z1, z2), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__U11(mark(z0), z1, z2), mark(x2))), MARK(x0)) MARK(plus(x0, plus(U12(z0, z1, z2), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__U12(mark(z0), z1, z2), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c10(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c10(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c10(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(U11(z0, z1, z2), plus(x1, x2))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), plus(x1, x2))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c10(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))) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c10(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c10(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c10(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(U11(x0, x1, x2), s(z0))) -> c10(A__PLUS(a__U11(mark(x0), x1, x2), s(mark(z0))), MARK(U11(x0, x1, x2))) MARK(plus(U11(x0, x1, x2), 0)) -> c10(A__PLUS(a__U11(mark(x0), x1, x2), 0), MARK(U11(x0, x1, x2))) MARK(plus(U11(x0, z1, z2), x3)) -> c10(A__PLUS(U11(mark(x0), z1, z2), mark(x3)), MARK(U11(x0, z1, z2))) MARK(plus(U11(U11(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(plus(U11(U12(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(plus(U11(plus(z0, z1), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(U11(plus(z0, z1), x1, x2))) MARK(plus(U11(tt, x1, x2), x3)) -> c10(A__PLUS(a__U11(tt, x1, x2), mark(x3)), MARK(U11(tt, x1, x2))) MARK(plus(U11(s(z0), x1, x2), x3)) -> c10(A__PLUS(a__U11(s(mark(z0)), x1, x2), mark(x3)), MARK(U11(s(z0), x1, x2))) MARK(plus(U11(x0, x1, x2), tt)) -> c10(MARK(U11(x0, x1, x2))) MARK(plus(U11(0, x1, x2), x3)) -> c10(A__PLUS(a__U11(0, x1, x2), mark(x3))) MARK(plus(U12(x0, x1, x2), s(z0))) -> c10(A__PLUS(a__U12(mark(x0), x1, x2), s(mark(z0))), MARK(U12(x0, x1, x2))) MARK(plus(U12(x0, x1, x2), 0)) -> c10(A__PLUS(a__U12(mark(x0), x1, x2), 0), MARK(U12(x0, x1, x2))) MARK(plus(U12(x0, z1, z2), x3)) -> c10(A__PLUS(U12(mark(x0), z1, z2), mark(x3)), MARK(U12(x0, z1, z2))) MARK(plus(U12(U11(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(plus(U12(U12(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(plus(U12(plus(z0, z1), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(U12(plus(z0, z1), x1, x2))) MARK(plus(U12(tt, x1, x2), x3)) -> c10(A__PLUS(a__U12(tt, x1, x2), mark(x3)), MARK(U12(tt, x1, x2))) MARK(plus(U12(s(z0), x1, x2), x3)) -> c10(A__PLUS(a__U12(s(mark(z0)), x1, x2), mark(x3)), MARK(U12(s(z0), x1, x2))) MARK(plus(U12(x0, x1, x2), tt)) -> c10(MARK(U12(x0, x1, x2))) MARK(plus(U12(0, x1, x2), x3)) -> c10(A__PLUS(a__U12(0, x1, x2), mark(x3))) MARK(plus(plus(x0, x1), s(z0))) -> c10(A__PLUS(a__plus(mark(x0), mark(x1)), s(mark(z0))), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), 0)) -> c10(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c10(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, U11(z0, z1, z2)), x2)) -> c10(A__PLUS(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), mark(x2)), MARK(plus(x0, U11(z0, z1, z2)))) MARK(plus(plus(x0, U12(z0, z1, z2)), x2)) -> c10(A__PLUS(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), mark(x2)), MARK(plus(x0, U12(z0, z1, z2)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c10(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)) -> c10(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, s(z0)), x2)) -> c10(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(x0, 0), x2)) -> c10(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(U11(z0, z1, z2), x1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(plus(U11(z0, z1, z2), x1))) MARK(plus(plus(U12(z0, z1, z2), x1), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(plus(U12(z0, z1, z2), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c10(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)) -> c10(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(0, x1), x2)) -> c10(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(x0, x1), tt)) -> c10(MARK(plus(x0, x1))) MARK(plus(s(x0), s(z0))) -> c10(A__PLUS(s(mark(x0)), s(mark(z0))), MARK(s(x0))) MARK(plus(s(x0), 0)) -> c10(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(U11(z0, z1, z2)), x1)) -> c10(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x1)), MARK(s(U11(z0, z1, z2)))) MARK(plus(s(U12(z0, z1, z2)), x1)) -> c10(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x1)), MARK(s(U12(z0, z1, z2)))) MARK(plus(s(plus(z0, z1)), x1)) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c10(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(s(z0)), x1)) -> c10(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(0), x1)) -> c10(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(x0), x1)) -> c10(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c10(MARK(s(x0))) MARK(plus(tt, s(z0))) -> c10(A__PLUS(tt, s(mark(z0)))) MARK(plus(tt, 0)) -> c10(A__PLUS(tt, 0)) MARK(plus(0, s(z0))) -> c10(A__PLUS(0, s(mark(z0)))) MARK(plus(0, 0)) -> c10(A__PLUS(0, 0)) MARK(plus(x0, U11(U11(z0, z1, z2), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(a__U11(mark(z0), z1, z2), x2, x3)), MARK(U11(U11(z0, z1, z2), x2, x3))) MARK(plus(x0, U11(U12(z0, z1, z2), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(a__U12(mark(z0), z1, z2), x2, x3)), MARK(U11(U12(z0, z1, z2), x2, x3))) MARK(plus(x0, U11(plus(z0, z1), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(U11(plus(z0, z1), x2, x3))) MARK(plus(x0, U11(tt, x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(tt, x2, x3)), MARK(U11(tt, x2, x3))) MARK(plus(x0, U11(s(z0), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(s(mark(z0)), x2, x3)), MARK(U11(s(z0), x2, x3))) MARK(plus(U11(z0, z1, z2), U11(x1, x2, x3))) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(U12(z0, z1, z2), U11(x1, x2, x3))) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(plus(z0, z1), U11(x1, x2, x3))) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(tt, U11(x1, x2, x3))) -> c11(A__PLUS(tt, a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(s(z0), U11(x1, x2, x3))) -> c11(A__PLUS(s(mark(z0)), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(0, U11(x1, x2, x3))) -> c11(A__PLUS(0, a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(x0, U11(x1, z1, z2))) -> c11(MARK(U11(x1, z1, z2))) MARK(plus(x0, U11(0, x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(0, x2, x3))) MARK(plus(x0, U12(U11(z0, z1, z2), x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(a__U11(mark(z0), z1, z2), x2, x3)), MARK(U12(U11(z0, z1, z2), x2, x3))) MARK(plus(x0, U12(U12(z0, z1, z2), x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(a__U12(mark(z0), z1, z2), x2, x3)), MARK(U12(U12(z0, z1, z2), x2, x3))) MARK(plus(x0, U12(plus(z0, z1), x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(U12(plus(z0, z1), x2, x3))) MARK(plus(x0, U12(tt, x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(tt, x2, x3)), MARK(U12(tt, x2, x3))) MARK(plus(x0, U12(s(z0), x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(s(mark(z0)), x2, x3)), MARK(U12(s(z0), x2, x3))) MARK(plus(U11(z0, z1, z2), U12(x1, x2, x3))) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(U12(z0, z1, z2), U12(x1, x2, x3))) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(plus(z0, z1), U12(x1, x2, x3))) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(tt, U12(x1, x2, x3))) -> c11(A__PLUS(tt, a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(s(z0), U12(x1, x2, x3))) -> c11(A__PLUS(s(mark(z0)), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(0, U12(x1, x2, x3))) -> c11(A__PLUS(0, a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(x0, U12(x1, z1, z2))) -> c11(MARK(U12(x1, z1, z2))) MARK(plus(x0, U12(0, x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(0, x2, x3))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_1, c9_1, c10_2, c10_1, c11_2, c11_1, c8_2, c9_2 ---------------------------------------- (209) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(x0, plus(z0, z1))) -> c11(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) by MARK(plus(x0, plus(x1, x2))) -> c11(A__PLUS(mark(x0), plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, U11(z0, z1, z2)))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), a__U11(mark(z0), z1, z2))), MARK(plus(x1, U11(z0, z1, z2)))) MARK(plus(x0, plus(x1, U12(z0, z1, z2)))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), a__U12(mark(z0), z1, z2))), MARK(plus(x1, U12(z0, z1, z2)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c11(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))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, s(z0)))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(x1, 0))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(U11(z0, z1, z2), x2))) -> c11(A__PLUS(mark(x0), a__plus(a__U11(mark(z0), z1, z2), mark(x2))), MARK(plus(U11(z0, z1, z2), x2))) MARK(plus(x0, plus(U12(z0, z1, z2), x2))) -> c11(A__PLUS(mark(x0), a__plus(a__U12(mark(z0), z1, z2), mark(x2))), MARK(plus(U12(z0, z1, z2), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c11(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))) -> c11(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c11(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(x0, plus(0, x2))) -> c11(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(U11(z0, z1, z2), plus(x1, x2))) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(U12(z0, z1, z2), plus(x1, x2))) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c11(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c11(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c11(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) ---------------------------------------- (210) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, 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c8(A__U11(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U11(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U11(U12(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U11(U12(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U11(U12(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U11(U12(x0, z1, z2), x3, x4)) -> c8(MARK(U12(x0, z1, z2))) MARK(U11(U12(0, x1, x2), x3, x4)) -> c8(A__U11(a__U12(0, x1, x2), x3, x4)) MARK(U11(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U11(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U11(plus(x0, plus(z0, z1)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U11(plus(x0, tt), x2, x3)) -> c8(A__U11(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U11(plus(x0, s(z0)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U11(plus(x0, 0), x2, x3)) -> c8(A__U11(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U11(plus(U11(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U11(plus(U12(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U11(plus(plus(z0, z1), x1), x2, x3)) -> c8(A__U11(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U11(plus(tt, x1), x2, x3)) -> c8(A__U11(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, 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MARK(U12(U11(0, x1, x2), x3, x4)) -> c9(A__U12(a__U11(0, x1, x2), x3, x4)) MARK(U12(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U12(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U12(U12(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U12(U12(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U12(U12(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U12(U12(x0, z1, z2), x3, x4)) -> c9(MARK(U12(x0, z1, z2))) MARK(U12(U12(0, x1, x2), x3, x4)) -> c9(A__U12(a__U12(0, x1, x2), x3, x4)) MARK(U12(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U12(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U12(plus(x0, plus(z0, z1)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U12(plus(x0, tt), x2, x3)) -> c9(A__U12(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U12(plus(x0, s(z0)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U12(plus(x0, 0), x2, x3)) -> c9(A__U12(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U12(plus(U11(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U12(plus(U12(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U12(plus(plus(z0, z1), x1), x2, x3)) -> c9(A__U12(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U12(plus(tt, x1), x2, x3)) -> c9(A__U12(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U12(plus(s(z0), x1), x2, x3)) -> c9(A__U12(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U12(plus(0, x1), x2, x3)) -> c9(A__U12(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U12(plus(x0, x1), x2, x3)) -> c9(MARK(plus(x0, x1))) MARK(plus(x0, U11(U11(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__U11(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U11(U12(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__U12(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U11(plus(z0, z1), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(tt, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U11(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U11(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(s(z0), U11(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(x0, U11(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U11(x1, x2, x3))) -> c10(A__PLUS(tt, a__U11(mark(x1), x2, x3))) MARK(plus(0, U11(x1, x2, x3))) -> c10(A__PLUS(0, a__U11(mark(x1), x2, x3))) MARK(plus(x0, U12(U11(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__U11(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U12(U12(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__U12(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U12(plus(z0, z1), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(x0)) MARK(plus(x0, U12(tt, x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U12(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U12(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U12(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U12(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U12(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(s(z0), U12(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(x0, U12(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U12(x1, x2, 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-> c10(MARK(s(x0))) MARK(plus(tt, s(z0))) -> c10(A__PLUS(tt, s(mark(z0)))) MARK(plus(tt, 0)) -> c10(A__PLUS(tt, 0)) MARK(plus(0, s(z0))) -> c10(A__PLUS(0, s(mark(z0)))) MARK(plus(0, 0)) -> c10(A__PLUS(0, 0)) MARK(plus(x0, U11(U11(z0, z1, z2), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(a__U11(mark(z0), z1, z2), x2, x3)), MARK(U11(U11(z0, z1, z2), x2, x3))) MARK(plus(x0, U11(U12(z0, z1, z2), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(a__U12(mark(z0), z1, z2), x2, x3)), MARK(U11(U12(z0, z1, z2), x2, x3))) MARK(plus(x0, U11(plus(z0, z1), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(U11(plus(z0, z1), x2, x3))) MARK(plus(x0, U11(tt, x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(tt, x2, x3)), MARK(U11(tt, x2, x3))) MARK(plus(x0, U11(s(z0), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(s(mark(z0)), x2, x3)), MARK(U11(s(z0), x2, x3))) MARK(plus(U11(z0, z1, z2), U11(x1, x2, x3))) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(U12(z0, z1, z2), U11(x1, x2, x3))) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(plus(z0, z1), U11(x1, x2, x3))) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(tt, U11(x1, x2, x3))) -> c11(A__PLUS(tt, a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(s(z0), U11(x1, x2, x3))) -> c11(A__PLUS(s(mark(z0)), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(0, U11(x1, x2, x3))) -> c11(A__PLUS(0, a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(x0, U11(x1, z1, z2))) -> c11(MARK(U11(x1, z1, z2))) MARK(plus(x0, U11(0, x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(0, x2, x3))) MARK(plus(x0, U12(U11(z0, z1, z2), x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(a__U11(mark(z0), z1, z2), x2, x3)), MARK(U12(U11(z0, z1, z2), x2, x3))) MARK(plus(x0, U12(U12(z0, z1, z2), x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(a__U12(mark(z0), z1, z2), x2, x3)), MARK(U12(U12(z0, z1, z2), x2, x3))) MARK(plus(x0, U12(plus(z0, z1), x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(U12(plus(z0, z1), x2, x3))) MARK(plus(x0, U12(tt, x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(tt, x2, x3)), MARK(U12(tt, x2, x3))) MARK(plus(x0, U12(s(z0), x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(s(mark(z0)), x2, x3)), MARK(U12(s(z0), x2, x3))) MARK(plus(U11(z0, z1, z2), U12(x1, x2, x3))) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(U12(z0, z1, z2), U12(x1, x2, x3))) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(plus(z0, z1), U12(x1, x2, x3))) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(tt, U12(x1, x2, x3))) -> c11(A__PLUS(tt, a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(s(z0), U12(x1, x2, x3))) -> c11(A__PLUS(s(mark(z0)), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(0, U12(x1, x2, x3))) -> c11(A__PLUS(0, a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(x0, U12(x1, z1, z2))) -> c11(MARK(U12(x1, z1, z2))) MARK(plus(x0, U12(0, x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(0, x2, x3))) MARK(plus(x0, plus(x1, x2))) -> c11(A__PLUS(mark(x0), plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, U11(z0, z1, z2)))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), a__U11(mark(z0), z1, z2))), MARK(plus(x1, U11(z0, z1, z2)))) MARK(plus(x0, plus(x1, U12(z0, z1, z2)))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), a__U12(mark(z0), z1, z2))), MARK(plus(x1, U12(z0, z1, z2)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c11(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))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, s(z0)))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(x1, 0))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(U11(z0, z1, z2), x2))) -> c11(A__PLUS(mark(x0), a__plus(a__U11(mark(z0), z1, z2), mark(x2))), MARK(plus(U11(z0, z1, z2), x2))) MARK(plus(x0, plus(U12(z0, z1, z2), x2))) -> c11(A__PLUS(mark(x0), a__plus(a__U12(mark(z0), z1, z2), mark(x2))), MARK(plus(U12(z0, z1, z2), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c11(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))) -> c11(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c11(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(x0, plus(0, x2))) -> c11(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(U11(z0, z1, z2), plus(x1, x2))) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(U12(z0, z1, z2), plus(x1, x2))) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c11(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c11(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c11(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, 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z1)), x2)) -> c10(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)) -> c10(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, s(z0)), x2)) -> c10(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(x0, 0), x2)) -> c10(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(U11(z0, z1, z2), x1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(plus(U11(z0, z1, z2), x1))) MARK(plus(plus(U12(z0, z1, z2), x1), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(plus(U12(z0, z1, z2), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c10(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)) -> c10(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(0, x1), x2)) -> c10(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(x0, x1), tt)) -> c10(MARK(plus(x0, x1))) MARK(plus(s(x0), s(z0))) -> c10(A__PLUS(s(mark(x0)), s(mark(z0))), MARK(s(x0))) MARK(plus(s(x0), 0)) -> c10(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(U11(z0, z1, z2)), x1)) -> c10(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x1)), MARK(s(U11(z0, z1, z2)))) MARK(plus(s(U12(z0, z1, z2)), x1)) -> c10(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x1)), MARK(s(U12(z0, z1, z2)))) MARK(plus(s(plus(z0, z1)), x1)) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c10(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(s(z0)), x1)) -> c10(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(0), x1)) -> c10(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(x0), x1)) -> c10(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c10(MARK(s(x0))) MARK(plus(tt, s(z0))) -> c10(A__PLUS(tt, s(mark(z0)))) MARK(plus(tt, 0)) -> c10(A__PLUS(tt, 0)) MARK(plus(0, s(z0))) -> c10(A__PLUS(0, s(mark(z0)))) MARK(plus(0, 0)) -> c10(A__PLUS(0, 0)) MARK(plus(x0, U11(U11(z0, z1, z2), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(a__U11(mark(z0), z1, z2), x2, x3)), MARK(U11(U11(z0, z1, z2), x2, x3))) MARK(plus(x0, U11(U12(z0, z1, z2), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(a__U12(mark(z0), z1, z2), x2, x3)), MARK(U11(U12(z0, z1, z2), x2, x3))) MARK(plus(x0, U11(plus(z0, z1), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(U11(plus(z0, z1), x2, x3))) MARK(plus(x0, U11(tt, x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(tt, x2, x3)), MARK(U11(tt, x2, x3))) MARK(plus(x0, U11(s(z0), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(s(mark(z0)), x2, x3)), MARK(U11(s(z0), x2, x3))) MARK(plus(U11(z0, z1, z2), U11(x1, x2, x3))) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(U12(z0, z1, z2), U11(x1, x2, x3))) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(plus(z0, z1), U11(x1, x2, x3))) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(tt, U11(x1, x2, x3))) -> c11(A__PLUS(tt, a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(s(z0), U11(x1, x2, x3))) -> c11(A__PLUS(s(mark(z0)), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(0, U11(x1, x2, x3))) -> c11(A__PLUS(0, a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(x0, U11(x1, z1, z2))) -> c11(MARK(U11(x1, z1, z2))) MARK(plus(x0, U11(0, x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(0, x2, x3))) MARK(plus(x0, U12(U11(z0, z1, z2), x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(a__U11(mark(z0), z1, z2), x2, x3)), MARK(U12(U11(z0, z1, z2), x2, x3))) MARK(plus(x0, U12(U12(z0, z1, z2), x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(a__U12(mark(z0), z1, z2), x2, x3)), MARK(U12(U12(z0, z1, z2), x2, x3))) MARK(plus(x0, U12(plus(z0, z1), x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(U12(plus(z0, z1), x2, x3))) MARK(plus(x0, U12(tt, x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(tt, x2, x3)), MARK(U12(tt, x2, x3))) MARK(plus(x0, U12(s(z0), x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(s(mark(z0)), x2, x3)), MARK(U12(s(z0), x2, x3))) MARK(plus(U11(z0, z1, z2), U12(x1, x2, x3))) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(U12(z0, z1, z2), U12(x1, x2, x3))) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(plus(z0, z1), U12(x1, x2, x3))) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(tt, U12(x1, x2, x3))) -> c11(A__PLUS(tt, a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(s(z0), U12(x1, x2, x3))) -> c11(A__PLUS(s(mark(z0)), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(0, U12(x1, x2, x3))) -> c11(A__PLUS(0, a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(x0, U12(x1, z1, z2))) -> c11(MARK(U12(x1, z1, z2))) MARK(plus(x0, U12(0, x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(0, x2, x3))) MARK(plus(x0, plus(x1, x2))) -> c11(A__PLUS(mark(x0), plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, U11(z0, z1, z2)))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), a__U11(mark(z0), z1, z2))), MARK(plus(x1, U11(z0, z1, z2)))) MARK(plus(x0, plus(x1, U12(z0, z1, z2)))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), a__U12(mark(z0), z1, z2))), MARK(plus(x1, U12(z0, z1, z2)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c11(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))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, s(z0)))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(x1, 0))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(U11(z0, z1, z2), x2))) -> c11(A__PLUS(mark(x0), a__plus(a__U11(mark(z0), z1, z2), mark(x2))), MARK(plus(U11(z0, z1, z2), x2))) MARK(plus(x0, plus(U12(z0, z1, z2), x2))) -> c11(A__PLUS(mark(x0), a__plus(a__U12(mark(z0), z1, z2), mark(x2))), MARK(plus(U12(z0, z1, z2), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c11(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))) -> c11(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c11(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(x0, plus(0, x2))) -> c11(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(U11(z0, z1, z2), plus(x1, x2))) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(U12(z0, z1, z2), plus(x1, x2))) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c11(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c11(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c11(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_1, c9_1, c10_2, c10_1, c11_2, c11_1, c8_2, c9_2 ---------------------------------------- (211) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (212) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), 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c11(A__PLUS(0, a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(x0, U12(x1, z1, z2))) -> c11(MARK(U12(x1, z1, z2))) MARK(plus(x0, U12(0, x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(0, x2, x3))) MARK(plus(x0, plus(x1, U11(z0, z1, z2)))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), a__U11(mark(z0), z1, z2))), MARK(plus(x1, U11(z0, z1, z2)))) MARK(plus(x0, plus(x1, U12(z0, z1, z2)))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), a__U12(mark(z0), z1, z2))), MARK(plus(x1, U12(z0, z1, z2)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c11(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))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, s(z0)))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(x1, 0))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(U11(z0, z1, z2), x2))) -> c11(A__PLUS(mark(x0), a__plus(a__U11(mark(z0), z1, z2), mark(x2))), MARK(plus(U11(z0, z1, z2), x2))) MARK(plus(x0, plus(U12(z0, z1, z2), x2))) -> c11(A__PLUS(mark(x0), a__plus(a__U12(mark(z0), z1, z2), mark(x2))), MARK(plus(U12(z0, z1, z2), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c11(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))) -> c11(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c11(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(x0, plus(0, x2))) -> c11(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(U11(z0, z1, z2), plus(x1, x2))) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(U12(z0, z1, z2), plus(x1, x2))) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c11(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c11(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c11(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c11(MARK(plus(x1, x2))) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, 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A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), 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c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U12(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c3(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c3(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U12(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U12(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U12(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, 0) -> c3(A__PLUS(0, 0)) MARK(U11(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U11(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U11(U11(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U11(U11(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U11(U11(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U11(U11(x0, z1, z2), x3, x4)) -> c8(MARK(U11(x0, z1, z2))) MARK(U11(U11(0, x1, x2), x3, x4)) -> c8(A__U11(a__U11(0, x1, x2), x3, x4)) MARK(U11(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U11(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U11(U12(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U11(U12(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U11(U12(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U11(U12(x0, z1, z2), x3, x4)) -> c8(MARK(U12(x0, z1, z2))) MARK(U11(U12(0, x1, x2), x3, x4)) -> c8(A__U11(a__U12(0, x1, x2), x3, x4)) MARK(U11(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U11(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U11(plus(x0, plus(z0, z1)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__plus(mark(z0), 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MARK(U11(plus(0, x1), x2, x3)) -> c8(A__U11(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U11(plus(x0, x1), x2, x3)) -> c8(MARK(plus(x0, x1))) MARK(U12(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U12(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U12(U11(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U12(U11(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U12(U11(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U12(U11(x0, z1, z2), x3, x4)) -> c9(MARK(U11(x0, z1, z2))) MARK(U12(U11(0, x1, x2), x3, x4)) -> c9(A__U12(a__U11(0, x1, x2), x3, x4)) MARK(U12(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U12(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U12(U12(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U12(U12(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U12(U12(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U12(U12(x0, z1, z2), x3, x4)) -> c9(MARK(U12(x0, z1, z2))) MARK(U12(U12(0, x1, x2), x3, x4)) -> c9(A__U12(a__U12(0, x1, x2), x3, x4)) MARK(U12(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U12(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U12(plus(x0, plus(z0, z1)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U12(plus(x0, tt), x2, x3)) -> c9(A__U12(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U12(plus(x0, s(z0)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U12(plus(x0, 0), x2, x3)) -> c9(A__U12(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U12(plus(U11(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U12(plus(U12(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U12(plus(plus(z0, z1), x1), x2, x3)) -> c9(A__U12(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U12(plus(tt, x1), x2, x3)) -> c9(A__U12(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U12(plus(s(z0), x1), x2, x3)) -> c9(A__U12(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U12(plus(0, x1), x2, x3)) -> c9(A__U12(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U12(plus(x0, x1), x2, x3)) -> c9(MARK(plus(x0, x1))) MARK(plus(x0, U11(U11(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__U11(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U11(U12(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__U12(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U11(plus(z0, z1), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(tt, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U11(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U11(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(s(z0), U11(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(x0, U11(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U11(x1, x2, x3))) -> c10(A__PLUS(tt, a__U11(mark(x1), x2, x3))) MARK(plus(0, U11(x1, x2, x3))) -> c10(A__PLUS(0, a__U11(mark(x1), x2, x3))) MARK(plus(x0, U12(U11(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__U11(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U12(U12(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__U12(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U12(plus(z0, z1), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(x0)) MARK(plus(x0, U12(tt, x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U12(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U12(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U12(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U12(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U12(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(s(z0), U12(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(x0, U12(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U12(x1, x2, x3))) -> c10(A__PLUS(tt, a__U12(mark(x1), x2, x3))) MARK(plus(0, U12(x1, x2, x3))) -> c10(A__PLUS(0, a__U12(mark(x1), x2, x3))) MARK(plus(x0, plus(x1, U11(z0, z1, z2)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__U11(mark(z0), z1, z2))), MARK(x0)) MARK(plus(x0, plus(x1, U12(z0, z1, z2)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__U12(mark(z0), z1, z2))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(U11(z0, z1, z2), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__U11(mark(z0), z1, z2), mark(x2))), MARK(x0)) MARK(plus(x0, plus(U12(z0, z1, z2), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__U12(mark(z0), z1, z2), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c10(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c10(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c10(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(U11(z0, z1, z2), plus(x1, x2))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), plus(x1, x2))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c10(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))) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c10(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c10(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c10(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(U11(x0, x1, x2), s(z0))) -> c10(A__PLUS(a__U11(mark(x0), x1, x2), s(mark(z0))), MARK(U11(x0, x1, x2))) MARK(plus(U11(x0, x1, x2), 0)) -> c10(A__PLUS(a__U11(mark(x0), x1, x2), 0), MARK(U11(x0, x1, x2))) MARK(plus(U11(x0, z1, z2), x3)) -> c10(A__PLUS(U11(mark(x0), z1, z2), mark(x3)), MARK(U11(x0, z1, z2))) MARK(plus(U11(U11(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(plus(U11(U12(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(plus(U11(plus(z0, z1), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(U11(plus(z0, z1), x1, x2))) MARK(plus(U11(tt, x1, x2), x3)) -> c10(A__PLUS(a__U11(tt, x1, x2), mark(x3)), MARK(U11(tt, x1, x2))) MARK(plus(U11(s(z0), x1, x2), x3)) -> c10(A__PLUS(a__U11(s(mark(z0)), x1, x2), mark(x3)), MARK(U11(s(z0), x1, x2))) MARK(plus(U11(x0, x1, x2), tt)) -> c10(MARK(U11(x0, x1, x2))) MARK(plus(U11(0, x1, x2), x3)) -> c10(A__PLUS(a__U11(0, x1, x2), mark(x3))) MARK(plus(U12(x0, x1, x2), s(z0))) -> c10(A__PLUS(a__U12(mark(x0), x1, x2), s(mark(z0))), MARK(U12(x0, x1, x2))) MARK(plus(U12(x0, x1, x2), 0)) -> c10(A__PLUS(a__U12(mark(x0), x1, x2), 0), MARK(U12(x0, x1, x2))) MARK(plus(U12(x0, z1, z2), x3)) -> c10(A__PLUS(U12(mark(x0), z1, z2), mark(x3)), MARK(U12(x0, z1, z2))) MARK(plus(U12(U11(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(plus(U12(U12(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(plus(U12(plus(z0, z1), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(U12(plus(z0, z1), x1, x2))) MARK(plus(U12(tt, x1, x2), x3)) -> c10(A__PLUS(a__U12(tt, x1, x2), mark(x3)), MARK(U12(tt, x1, x2))) MARK(plus(U12(s(z0), x1, x2), x3)) -> c10(A__PLUS(a__U12(s(mark(z0)), x1, x2), mark(x3)), MARK(U12(s(z0), x1, x2))) MARK(plus(U12(x0, x1, x2), tt)) -> c10(MARK(U12(x0, x1, x2))) MARK(plus(U12(0, x1, x2), x3)) -> c10(A__PLUS(a__U12(0, x1, x2), mark(x3))) MARK(plus(plus(x0, x1), s(z0))) -> c10(A__PLUS(a__plus(mark(x0), mark(x1)), s(mark(z0))), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), 0)) -> c10(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c10(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, U11(z0, z1, z2)), x2)) -> c10(A__PLUS(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), mark(x2)), MARK(plus(x0, U11(z0, z1, z2)))) MARK(plus(plus(x0, U12(z0, z1, z2)), x2)) -> c10(A__PLUS(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), mark(x2)), MARK(plus(x0, U12(z0, z1, z2)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c10(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)) -> c10(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, s(z0)), x2)) -> c10(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(x0, 0), x2)) -> c10(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(U11(z0, z1, z2), x1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(plus(U11(z0, z1, z2), x1))) MARK(plus(plus(U12(z0, z1, z2), x1), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(plus(U12(z0, z1, z2), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c10(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)) -> c10(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(0, x1), x2)) -> c10(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(x0, x1), tt)) -> c10(MARK(plus(x0, x1))) MARK(plus(s(x0), s(z0))) -> c10(A__PLUS(s(mark(x0)), s(mark(z0))), MARK(s(x0))) MARK(plus(s(x0), 0)) -> c10(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(U11(z0, z1, z2)), x1)) -> c10(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x1)), MARK(s(U11(z0, z1, z2)))) MARK(plus(s(U12(z0, z1, z2)), x1)) -> c10(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x1)), MARK(s(U12(z0, z1, z2)))) MARK(plus(s(plus(z0, z1)), x1)) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c10(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(s(z0)), x1)) -> c10(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(0), x1)) -> c10(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(x0), x1)) -> c10(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c10(MARK(s(x0))) MARK(plus(tt, s(z0))) -> c10(A__PLUS(tt, s(mark(z0)))) MARK(plus(tt, 0)) -> c10(A__PLUS(tt, 0)) MARK(plus(0, s(z0))) -> c10(A__PLUS(0, s(mark(z0)))) MARK(plus(0, 0)) -> c10(A__PLUS(0, 0)) MARK(plus(x0, U11(U11(z0, z1, z2), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(a__U11(mark(z0), z1, z2), x2, x3)), MARK(U11(U11(z0, z1, z2), x2, x3))) MARK(plus(x0, U11(U12(z0, z1, z2), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(a__U12(mark(z0), z1, z2), x2, x3)), MARK(U11(U12(z0, z1, z2), x2, x3))) MARK(plus(x0, U11(plus(z0, z1), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(U11(plus(z0, z1), x2, x3))) MARK(plus(x0, U11(tt, x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(tt, x2, x3)), MARK(U11(tt, x2, x3))) MARK(plus(x0, U11(s(z0), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(s(mark(z0)), x2, x3)), MARK(U11(s(z0), x2, x3))) MARK(plus(U11(z0, z1, z2), U11(x1, x2, x3))) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(U12(z0, z1, z2), U11(x1, x2, x3))) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(plus(z0, z1), U11(x1, x2, x3))) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(tt, U11(x1, x2, x3))) -> c11(A__PLUS(tt, a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(s(z0), U11(x1, x2, x3))) -> c11(A__PLUS(s(mark(z0)), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(0, U11(x1, x2, x3))) -> c11(A__PLUS(0, a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(x0, U11(x1, z1, z2))) -> c11(MARK(U11(x1, z1, z2))) MARK(plus(x0, U11(0, x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(0, x2, x3))) MARK(plus(x0, U12(U11(z0, z1, z2), x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(a__U11(mark(z0), z1, z2), x2, x3)), MARK(U12(U11(z0, z1, z2), x2, x3))) MARK(plus(x0, U12(U12(z0, z1, z2), x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(a__U12(mark(z0), z1, z2), x2, x3)), MARK(U12(U12(z0, z1, z2), x2, x3))) MARK(plus(x0, U12(plus(z0, z1), x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(U12(plus(z0, z1), x2, x3))) MARK(plus(x0, U12(tt, x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(tt, x2, x3)), MARK(U12(tt, x2, x3))) MARK(plus(x0, U12(s(z0), x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(s(mark(z0)), x2, x3)), MARK(U12(s(z0), x2, x3))) MARK(plus(U11(z0, z1, z2), U12(x1, x2, x3))) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(U12(z0, z1, z2), U12(x1, x2, x3))) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(plus(z0, z1), U12(x1, x2, x3))) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(tt, U12(x1, x2, x3))) -> c11(A__PLUS(tt, a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(s(z0), U12(x1, x2, x3))) -> c11(A__PLUS(s(mark(z0)), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(0, U12(x1, x2, x3))) -> c11(A__PLUS(0, a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(x0, U12(x1, z1, z2))) -> c11(MARK(U12(x1, z1, z2))) MARK(plus(x0, U12(0, x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(0, x2, x3))) MARK(plus(x0, plus(x1, U11(z0, z1, z2)))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), a__U11(mark(z0), z1, z2))), MARK(plus(x1, U11(z0, z1, z2)))) MARK(plus(x0, plus(x1, U12(z0, z1, z2)))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), a__U12(mark(z0), z1, z2))), MARK(plus(x1, U12(z0, z1, z2)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c11(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))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, s(z0)))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(x1, 0))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(U11(z0, z1, z2), x2))) -> c11(A__PLUS(mark(x0), a__plus(a__U11(mark(z0), z1, z2), mark(x2))), MARK(plus(U11(z0, z1, z2), x2))) MARK(plus(x0, plus(U12(z0, z1, z2), x2))) -> c11(A__PLUS(mark(x0), a__plus(a__U12(mark(z0), z1, z2), mark(x2))), MARK(plus(U12(z0, z1, z2), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c11(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))) -> c11(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c11(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(x0, plus(0, x2))) -> c11(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(U11(z0, z1, z2), plus(x1, x2))) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(U12(z0, z1, z2), plus(x1, x2))) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c11(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c11(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c11(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c11(MARK(plus(x1, x2))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_1, c9_1, c10_2, c10_1, c11_2, c11_1, c8_2, c9_2 ---------------------------------------- (213) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(U11(z0, z1, z2), x1)) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) by MARK(plus(U11(x0, x1, x2), U11(z0, z1, z2))) -> c11(A__PLUS(a__U11(mark(x0), x1, x2), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(U11(x0, x1, x2), U12(z0, z1, z2))) -> c11(A__PLUS(a__U11(mark(x0), x1, x2), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(U11(x0, x1, x2), plus(z0, z1))) -> c11(A__PLUS(a__U11(mark(x0), x1, x2), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(U11(x0, x1, x2), tt)) -> c11(A__PLUS(a__U11(mark(x0), x1, x2), tt), MARK(tt)) MARK(plus(U11(x0, x1, x2), s(z0))) -> c11(A__PLUS(a__U11(mark(x0), x1, x2), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(x0, x1, x2), 0)) -> c11(A__PLUS(a__U11(mark(x0), x1, x2), 0), MARK(0)) MARK(plus(U11(x0, z1, z2), x3)) -> c11(A__PLUS(U11(mark(x0), z1, z2), mark(x3)), MARK(x3)) MARK(plus(U11(U11(z0, z1, z2), x1, x2), x3)) -> c11(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(U12(z0, z1, z2), x1, x2), x3)) -> c11(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(plus(z0, z1), x1, x2), x3)) -> c11(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(tt, x1, x2), x3)) -> c11(A__PLUS(a__U11(tt, x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(s(z0), x1, x2), x3)) -> c11(A__PLUS(a__U11(s(mark(z0)), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(0, x1, x2), x3)) -> c11(A__PLUS(a__U11(0, x1, x2), mark(x3)), MARK(x3)) ---------------------------------------- (214) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U12(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c3(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c3(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U12(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U12(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U12(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, 0) -> c3(A__PLUS(0, 0)) MARK(U11(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U11(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U11(U11(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U11(U11(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U11(U11(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U11(U11(x0, z1, z2), x3, x4)) -> c8(MARK(U11(x0, z1, z2))) MARK(U11(U11(0, x1, x2), x3, x4)) -> c8(A__U11(a__U11(0, x1, x2), x3, x4)) MARK(U11(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U11(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U11(U12(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U11(U12(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U11(U12(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U11(U12(x0, z1, z2), x3, x4)) -> c8(MARK(U12(x0, z1, z2))) MARK(U11(U12(0, x1, x2), x3, x4)) -> c8(A__U11(a__U12(0, x1, x2), x3, x4)) MARK(U11(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U11(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U11(plus(x0, plus(z0, z1)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U11(plus(x0, tt), x2, x3)) -> c8(A__U11(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U11(plus(x0, s(z0)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U11(plus(x0, 0), x2, x3)) -> c8(A__U11(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U11(plus(U11(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U11(plus(U12(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U11(plus(plus(z0, z1), x1), x2, x3)) -> c8(A__U11(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U11(plus(tt, x1), x2, x3)) -> c8(A__U11(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U11(plus(s(z0), x1), x2, x3)) -> c8(A__U11(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U11(plus(0, x1), x2, x3)) -> c8(A__U11(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U11(plus(x0, x1), x2, x3)) -> c8(MARK(plus(x0, x1))) MARK(U12(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U12(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U12(U11(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U12(U11(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U12(U11(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U12(U11(x0, z1, z2), x3, x4)) -> c9(MARK(U11(x0, z1, z2))) MARK(U12(U11(0, x1, x2), x3, x4)) -> c9(A__U12(a__U11(0, x1, x2), x3, x4)) MARK(U12(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U12(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U12(U12(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U12(U12(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U12(U12(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U12(U12(x0, z1, z2), x3, x4)) -> c9(MARK(U12(x0, z1, z2))) MARK(U12(U12(0, x1, x2), x3, x4)) -> c9(A__U12(a__U12(0, x1, x2), x3, x4)) MARK(U12(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U12(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U12(plus(x0, plus(z0, z1)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U12(plus(x0, tt), x2, x3)) -> c9(A__U12(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U12(plus(x0, s(z0)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U12(plus(x0, 0), x2, x3)) -> c9(A__U12(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U12(plus(U11(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U12(plus(U12(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U12(plus(plus(z0, z1), x1), x2, x3)) -> c9(A__U12(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U12(plus(tt, x1), x2, x3)) -> c9(A__U12(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U12(plus(s(z0), x1), x2, x3)) -> c9(A__U12(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U12(plus(0, x1), x2, x3)) -> c9(A__U12(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U12(plus(x0, x1), x2, x3)) -> c9(MARK(plus(x0, x1))) MARK(plus(x0, U11(U11(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__U11(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U11(U12(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__U12(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U11(plus(z0, z1), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(tt, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U11(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U11(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(s(z0), U11(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(x0, U11(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U11(x1, x2, x3))) -> c10(A__PLUS(tt, a__U11(mark(x1), x2, x3))) MARK(plus(0, U11(x1, x2, x3))) -> c10(A__PLUS(0, a__U11(mark(x1), x2, x3))) MARK(plus(x0, U12(U11(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__U11(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U12(U12(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__U12(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U12(plus(z0, z1), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(x0)) MARK(plus(x0, U12(tt, x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U12(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U12(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U12(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U12(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U12(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(s(z0), U12(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(x0, U12(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U12(x1, x2, x3))) -> c10(A__PLUS(tt, a__U12(mark(x1), x2, x3))) MARK(plus(0, U12(x1, x2, x3))) -> c10(A__PLUS(0, a__U12(mark(x1), x2, x3))) MARK(plus(x0, plus(x1, U11(z0, z1, z2)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__U11(mark(z0), z1, z2))), MARK(x0)) MARK(plus(x0, plus(x1, U12(z0, z1, z2)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__U12(mark(z0), z1, z2))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(U11(z0, z1, z2), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__U11(mark(z0), z1, z2), mark(x2))), MARK(x0)) MARK(plus(x0, plus(U12(z0, z1, z2), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__U12(mark(z0), z1, z2), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c10(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c10(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c10(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c10(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(U11(z0, z1, z2), plus(x1, x2))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), plus(x1, x2))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c10(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))) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c10(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c10(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c10(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(U11(x0, x1, x2), s(z0))) -> c10(A__PLUS(a__U11(mark(x0), x1, x2), s(mark(z0))), MARK(U11(x0, x1, x2))) MARK(plus(U11(x0, x1, x2), 0)) -> c10(A__PLUS(a__U11(mark(x0), x1, x2), 0), MARK(U11(x0, x1, x2))) MARK(plus(U11(x0, z1, z2), x3)) -> c10(A__PLUS(U11(mark(x0), z1, z2), mark(x3)), MARK(U11(x0, z1, z2))) MARK(plus(U11(U11(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(plus(U11(U12(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(plus(U11(plus(z0, z1), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(U11(plus(z0, z1), x1, x2))) MARK(plus(U11(tt, x1, x2), x3)) -> c10(A__PLUS(a__U11(tt, x1, x2), mark(x3)), MARK(U11(tt, x1, x2))) MARK(plus(U11(s(z0), x1, x2), x3)) -> c10(A__PLUS(a__U11(s(mark(z0)), x1, x2), mark(x3)), MARK(U11(s(z0), x1, x2))) MARK(plus(U11(x0, x1, x2), tt)) -> c10(MARK(U11(x0, x1, x2))) MARK(plus(U11(0, x1, x2), x3)) -> c10(A__PLUS(a__U11(0, x1, x2), mark(x3))) MARK(plus(U12(x0, x1, x2), s(z0))) -> c10(A__PLUS(a__U12(mark(x0), x1, x2), s(mark(z0))), MARK(U12(x0, x1, x2))) MARK(plus(U12(x0, x1, x2), 0)) -> c10(A__PLUS(a__U12(mark(x0), x1, x2), 0), MARK(U12(x0, x1, x2))) MARK(plus(U12(x0, z1, z2), x3)) -> c10(A__PLUS(U12(mark(x0), z1, z2), mark(x3)), MARK(U12(x0, z1, z2))) MARK(plus(U12(U11(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(plus(U12(U12(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U12(U12(z0, 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MARK(U12(U11(z0, z1, z2), x2, x3))) MARK(plus(x0, U12(U12(z0, z1, z2), x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(a__U12(mark(z0), z1, z2), x2, x3)), MARK(U12(U12(z0, z1, z2), x2, x3))) MARK(plus(x0, U12(plus(z0, z1), x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(U12(plus(z0, z1), x2, x3))) MARK(plus(x0, U12(tt, x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(tt, x2, x3)), MARK(U12(tt, x2, x3))) MARK(plus(x0, U12(s(z0), x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(s(mark(z0)), x2, x3)), MARK(U12(s(z0), x2, x3))) MARK(plus(U11(z0, z1, z2), U12(x1, x2, x3))) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(U12(z0, z1, z2), U12(x1, x2, x3))) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(plus(z0, z1), U12(x1, x2, x3))) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(tt, U12(x1, x2, x3))) -> 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c11(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(x1, 0))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(U11(z0, z1, z2), x2))) -> c11(A__PLUS(mark(x0), a__plus(a__U11(mark(z0), z1, z2), mark(x2))), MARK(plus(U11(z0, z1, z2), x2))) MARK(plus(x0, plus(U12(z0, z1, z2), x2))) -> c11(A__PLUS(mark(x0), a__plus(a__U12(mark(z0), z1, z2), mark(x2))), MARK(plus(U12(z0, z1, z2), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c11(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))) -> c11(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c11(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(x0, plus(0, x2))) -> c11(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(U11(z0, z1, z2), plus(x1, x2))) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), 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c11(A__PLUS(U11(mark(x0), z1, z2), mark(x3)), MARK(x3)) MARK(plus(U11(U11(z0, z1, z2), x1, x2), x3)) -> c11(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(U12(z0, z1, z2), x1, x2), x3)) -> c11(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(plus(z0, z1), x1, x2), x3)) -> c11(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(tt, x1, x2), x3)) -> c11(A__PLUS(a__U11(tt, x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(s(z0), x1, x2), x3)) -> c11(A__PLUS(a__U11(s(mark(z0)), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(0, x1, x2), x3)) -> c11(A__PLUS(a__U11(0, x1, x2), mark(x3)), MARK(x3)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, 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z1)), x2)) -> c10(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)) -> c10(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, s(z0)), x2)) -> c10(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(x0, 0), x2)) -> c10(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(U11(z0, z1, z2), x1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(plus(U11(z0, z1, z2), x1))) MARK(plus(plus(U12(z0, z1, z2), x1), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(plus(U12(z0, z1, z2), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c10(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)) -> c10(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(0, x1), x2)) -> c10(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(x0, x1), tt)) -> c10(MARK(plus(x0, x1))) MARK(plus(s(x0), s(z0))) -> c10(A__PLUS(s(mark(x0)), s(mark(z0))), MARK(s(x0))) MARK(plus(s(x0), 0)) -> c10(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(U11(z0, z1, z2)), x1)) -> c10(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x1)), MARK(s(U11(z0, z1, z2)))) MARK(plus(s(U12(z0, z1, z2)), x1)) -> c10(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x1)), MARK(s(U12(z0, z1, z2)))) MARK(plus(s(plus(z0, z1)), x1)) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c10(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(s(z0)), x1)) -> c10(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(0), x1)) -> c10(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(x0), x1)) -> c10(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c10(MARK(s(x0))) MARK(plus(tt, s(z0))) -> c10(A__PLUS(tt, s(mark(z0)))) MARK(plus(tt, 0)) -> c10(A__PLUS(tt, 0)) MARK(plus(0, s(z0))) -> c10(A__PLUS(0, s(mark(z0)))) MARK(plus(0, 0)) -> c10(A__PLUS(0, 0)) MARK(plus(x0, U11(U11(z0, z1, z2), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(a__U11(mark(z0), z1, z2), x2, x3)), MARK(U11(U11(z0, z1, z2), x2, x3))) MARK(plus(x0, U11(U12(z0, z1, z2), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(a__U12(mark(z0), z1, z2), x2, x3)), MARK(U11(U12(z0, z1, z2), x2, x3))) MARK(plus(x0, U11(plus(z0, z1), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(U11(plus(z0, z1), x2, x3))) MARK(plus(x0, U11(tt, x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(tt, x2, x3)), MARK(U11(tt, x2, x3))) MARK(plus(x0, U11(s(z0), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(s(mark(z0)), x2, x3)), MARK(U11(s(z0), x2, x3))) MARK(plus(U11(z0, z1, z2), U11(x1, x2, x3))) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(U12(z0, z1, z2), U11(x1, x2, x3))) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(plus(z0, z1), U11(x1, x2, x3))) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(tt, U11(x1, x2, x3))) -> c11(A__PLUS(tt, a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(s(z0), U11(x1, x2, x3))) -> c11(A__PLUS(s(mark(z0)), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(0, U11(x1, x2, x3))) -> c11(A__PLUS(0, a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(x0, U11(x1, z1, z2))) -> c11(MARK(U11(x1, z1, z2))) MARK(plus(x0, U11(0, x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(0, x2, x3))) MARK(plus(x0, U12(U11(z0, z1, z2), x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(a__U11(mark(z0), z1, z2), x2, x3)), MARK(U12(U11(z0, z1, z2), x2, x3))) MARK(plus(x0, U12(U12(z0, z1, z2), x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(a__U12(mark(z0), z1, z2), x2, x3)), MARK(U12(U12(z0, z1, z2), x2, x3))) MARK(plus(x0, U12(plus(z0, z1), x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(U12(plus(z0, z1), x2, x3))) MARK(plus(x0, U12(tt, x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(tt, x2, x3)), MARK(U12(tt, x2, x3))) MARK(plus(x0, U12(s(z0), x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(s(mark(z0)), x2, x3)), MARK(U12(s(z0), x2, x3))) MARK(plus(U11(z0, z1, z2), U12(x1, x2, x3))) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(U12(z0, z1, z2), U12(x1, x2, x3))) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(plus(z0, z1), U12(x1, x2, x3))) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(tt, U12(x1, x2, x3))) -> c11(A__PLUS(tt, a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(s(z0), U12(x1, x2, x3))) -> c11(A__PLUS(s(mark(z0)), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(0, U12(x1, x2, x3))) -> c11(A__PLUS(0, a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(x0, U12(x1, z1, z2))) -> c11(MARK(U12(x1, z1, z2))) MARK(plus(x0, U12(0, x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(0, x2, x3))) MARK(plus(x0, plus(x1, U11(z0, z1, z2)))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), a__U11(mark(z0), z1, z2))), MARK(plus(x1, U11(z0, z1, z2)))) MARK(plus(x0, plus(x1, U12(z0, z1, z2)))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), a__U12(mark(z0), z1, z2))), MARK(plus(x1, U12(z0, z1, z2)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c11(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))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, s(z0)))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(x1, 0))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(U11(z0, z1, z2), x2))) -> c11(A__PLUS(mark(x0), a__plus(a__U11(mark(z0), z1, z2), mark(x2))), MARK(plus(U11(z0, z1, z2), x2))) MARK(plus(x0, plus(U12(z0, z1, z2), x2))) -> c11(A__PLUS(mark(x0), a__plus(a__U12(mark(z0), z1, z2), mark(x2))), MARK(plus(U12(z0, z1, z2), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c11(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))) -> c11(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c11(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(x0, plus(0, x2))) -> c11(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(U11(z0, z1, z2), plus(x1, x2))) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(U12(z0, z1, z2), plus(x1, x2))) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c11(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c11(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c11(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c11(MARK(plus(x1, x2))) MARK(plus(U11(x0, x1, x2), tt)) -> c11(A__PLUS(a__U11(mark(x0), x1, x2), tt), MARK(tt)) MARK(plus(U11(x0, x1, x2), s(z0))) -> c11(A__PLUS(a__U11(mark(x0), x1, x2), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(x0, x1, x2), 0)) -> c11(A__PLUS(a__U11(mark(x0), x1, x2), 0), MARK(0)) MARK(plus(U11(x0, z1, z2), x3)) -> c11(A__PLUS(U11(mark(x0), z1, z2), mark(x3)), MARK(x3)) MARK(plus(U11(U11(z0, z1, z2), x1, x2), x3)) -> c11(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(U12(z0, z1, z2), x1, x2), x3)) -> c11(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(plus(z0, z1), x1, x2), x3)) -> c11(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(tt, x1, x2), x3)) -> c11(A__PLUS(a__U11(tt, x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(s(z0), x1, x2), x3)) -> c11(A__PLUS(a__U11(s(mark(z0)), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(0, x1, x2), x3)) -> c11(A__PLUS(a__U11(0, x1, x2), mark(x3)), MARK(x3)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_1, c9_1, c10_2, c10_1, c11_2, c11_1, c8_2, c9_2 ---------------------------------------- (215) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(plus(U11(x0, x1, x2), tt)) -> c11(A__PLUS(a__U11(mark(x0), x1, x2), tt), MARK(tt)) ---------------------------------------- (216) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), 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A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U12(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c3(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c3(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U12(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U12(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U12(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, 0) -> c3(A__PLUS(0, 0)) MARK(U11(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U11(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U11(U11(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U11(U11(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U11(U11(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U11(U11(x0, z1, z2), x3, x4)) -> c8(MARK(U11(x0, z1, z2))) MARK(U11(U11(0, x1, x2), x3, x4)) -> c8(A__U11(a__U11(0, x1, x2), x3, x4)) MARK(U11(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U11(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U11(U12(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U11(U12(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U11(U12(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U11(U12(x0, z1, z2), x3, x4)) -> c8(MARK(U12(x0, z1, z2))) MARK(U11(U12(0, x1, x2), x3, x4)) -> c8(A__U11(a__U12(0, x1, x2), x3, x4)) MARK(U11(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U11(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U11(plus(x0, plus(z0, z1)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U11(plus(x0, tt), x2, x3)) -> c8(A__U11(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U11(plus(x0, s(z0)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U11(plus(x0, 0), x2, x3)) -> c8(A__U11(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U11(plus(U11(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U11(plus(U12(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U11(plus(plus(z0, z1), x1), x2, x3)) -> c8(A__U11(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U11(plus(tt, x1), x2, x3)) -> c8(A__U11(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U11(plus(s(z0), x1), x2, x3)) -> c8(A__U11(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U11(plus(0, x1), x2, x3)) -> c8(A__U11(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U11(plus(x0, x1), x2, x3)) -> c8(MARK(plus(x0, x1))) MARK(U12(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U12(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U12(U11(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U12(U11(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U12(U11(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U12(U11(x0, z1, z2), x3, x4)) -> c9(MARK(U11(x0, z1, z2))) MARK(U12(U11(0, x1, x2), x3, x4)) -> c9(A__U12(a__U11(0, x1, x2), x3, x4)) MARK(U12(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> 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MARK(U12(plus(z0, z1), x2, x3))) MARK(plus(x0, U12(tt, x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(tt, x2, x3)), MARK(U12(tt, x2, x3))) MARK(plus(x0, U12(s(z0), x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(s(mark(z0)), x2, x3)), MARK(U12(s(z0), x2, x3))) MARK(plus(U11(z0, z1, z2), U12(x1, x2, x3))) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(U12(z0, z1, z2), U12(x1, x2, x3))) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(plus(z0, z1), U12(x1, x2, x3))) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(tt, U12(x1, x2, x3))) -> c11(A__PLUS(tt, a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(s(z0), U12(x1, x2, x3))) -> c11(A__PLUS(s(mark(z0)), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(0, U12(x1, x2, x3))) -> c11(A__PLUS(0, a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(x0, U12(x1, z1, z2))) -> c11(MARK(U12(x1, z1, z2))) MARK(plus(x0, U12(0, x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(0, x2, x3))) MARK(plus(x0, plus(x1, U11(z0, z1, z2)))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), a__U11(mark(z0), z1, z2))), MARK(plus(x1, U11(z0, z1, z2)))) MARK(plus(x0, plus(x1, U12(z0, z1, z2)))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), a__U12(mark(z0), z1, z2))), MARK(plus(x1, U12(z0, z1, z2)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c11(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))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, s(z0)))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(x1, 0))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(U11(z0, z1, z2), x2))) -> c11(A__PLUS(mark(x0), a__plus(a__U11(mark(z0), z1, z2), mark(x2))), MARK(plus(U11(z0, z1, z2), x2))) MARK(plus(x0, plus(U12(z0, z1, z2), x2))) -> c11(A__PLUS(mark(x0), a__plus(a__U12(mark(z0), z1, z2), mark(x2))), MARK(plus(U12(z0, z1, z2), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c11(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))) -> c11(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c11(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(x0, plus(0, x2))) -> c11(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(U11(z0, z1, z2), plus(x1, x2))) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(U12(z0, z1, z2), plus(x1, x2))) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c11(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c11(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c11(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c11(MARK(plus(x1, x2))) MARK(plus(U11(x0, x1, x2), s(z0))) -> c11(A__PLUS(a__U11(mark(x0), x1, x2), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(x0, x1, x2), 0)) -> c11(A__PLUS(a__U11(mark(x0), x1, x2), 0), MARK(0)) MARK(plus(U11(x0, z1, z2), x3)) -> c11(A__PLUS(U11(mark(x0), z1, z2), mark(x3)), MARK(x3)) MARK(plus(U11(U11(z0, z1, z2), x1, x2), x3)) -> c11(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(U12(z0, z1, z2), x1, x2), x3)) -> c11(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(plus(z0, z1), x1, x2), x3)) -> c11(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(tt, x1, x2), x3)) -> c11(A__PLUS(a__U11(tt, x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(s(z0), x1, x2), x3)) -> c11(A__PLUS(a__U11(s(mark(z0)), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(0, x1, x2), x3)) -> c11(A__PLUS(a__U11(0, x1, x2), mark(x3)), MARK(x3)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), 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a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) 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U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), 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MARK(plus(U11(z0, z1, z2), U12(x1, x2, x3))) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(U12(z0, z1, z2), U12(x1, x2, x3))) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(plus(z0, z1), U12(x1, x2, x3))) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(tt, U12(x1, x2, x3))) -> c11(A__PLUS(tt, a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(s(z0), U12(x1, x2, x3))) -> c11(A__PLUS(s(mark(z0)), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(0, U12(x1, x2, x3))) -> c11(A__PLUS(0, a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(x0, U12(x1, z1, z2))) -> c11(MARK(U12(x1, z1, z2))) MARK(plus(x0, U12(0, x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(0, x2, x3))) MARK(plus(x0, plus(x1, U11(z0, z1, z2)))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), a__U11(mark(z0), z1, z2))), MARK(plus(x1, U11(z0, z1, z2)))) MARK(plus(x0, plus(x1, U12(z0, z1, z2)))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), a__U12(mark(z0), z1, z2))), MARK(plus(x1, U12(z0, z1, z2)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c11(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))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, s(z0)))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(x1, 0))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(U11(z0, z1, z2), x2))) -> c11(A__PLUS(mark(x0), a__plus(a__U11(mark(z0), z1, z2), mark(x2))), MARK(plus(U11(z0, z1, z2), x2))) MARK(plus(x0, plus(U12(z0, z1, z2), x2))) -> c11(A__PLUS(mark(x0), a__plus(a__U12(mark(z0), z1, z2), mark(x2))), MARK(plus(U12(z0, z1, z2), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c11(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))) -> c11(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c11(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(x0, plus(0, x2))) -> c11(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(U11(z0, z1, z2), plus(x1, x2))) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(U12(z0, z1, z2), plus(x1, x2))) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c11(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c11(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c11(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c11(MARK(plus(x1, x2))) MARK(plus(U11(x0, x1, x2), s(z0))) -> c11(A__PLUS(a__U11(mark(x0), x1, x2), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(x0, x1, x2), 0)) -> c11(A__PLUS(a__U11(mark(x0), x1, x2), 0), MARK(0)) MARK(plus(U11(x0, z1, z2), x3)) -> c11(A__PLUS(U11(mark(x0), z1, z2), mark(x3)), MARK(x3)) MARK(plus(U11(U11(z0, z1, z2), x1, x2), x3)) -> c11(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(U12(z0, z1, z2), x1, x2), x3)) -> c11(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(plus(z0, z1), x1, x2), x3)) -> c11(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(tt, x1, x2), x3)) -> c11(A__PLUS(a__U11(tt, x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(s(z0), x1, x2), x3)) -> c11(A__PLUS(a__U11(s(mark(z0)), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(0, x1, x2), x3)) -> c11(A__PLUS(a__U11(0, x1, x2), mark(x3)), MARK(x3)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_1, c9_1, c10_2, c10_1, c11_2, c11_1, c8_2, c9_2 ---------------------------------------- (217) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (218) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U12(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c3(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(U12(z0, z1, z2))) -> 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MARK(plus(U11(U12(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(plus(U11(plus(z0, z1), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(U11(plus(z0, z1), x1, x2))) MARK(plus(U11(tt, x1, x2), x3)) -> c10(A__PLUS(a__U11(tt, x1, x2), mark(x3)), MARK(U11(tt, x1, x2))) MARK(plus(U11(s(z0), x1, x2), x3)) -> c10(A__PLUS(a__U11(s(mark(z0)), x1, x2), mark(x3)), MARK(U11(s(z0), x1, x2))) MARK(plus(U11(x0, x1, x2), tt)) -> c10(MARK(U11(x0, x1, x2))) MARK(plus(U11(0, x1, x2), x3)) -> c10(A__PLUS(a__U11(0, x1, x2), mark(x3))) MARK(plus(U12(x0, x1, x2), s(z0))) -> c10(A__PLUS(a__U12(mark(x0), x1, x2), s(mark(z0))), MARK(U12(x0, x1, x2))) MARK(plus(U12(x0, x1, x2), 0)) -> c10(A__PLUS(a__U12(mark(x0), x1, x2), 0), MARK(U12(x0, x1, x2))) MARK(plus(U12(x0, z1, z2), x3)) -> c10(A__PLUS(U12(mark(x0), z1, z2), mark(x3)), MARK(U12(x0, z1, z2))) MARK(plus(U12(U11(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(plus(U12(U12(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(plus(U12(plus(z0, z1), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(U12(plus(z0, z1), x1, x2))) MARK(plus(U12(tt, x1, x2), x3)) -> c10(A__PLUS(a__U12(tt, x1, x2), mark(x3)), MARK(U12(tt, x1, x2))) MARK(plus(U12(s(z0), x1, x2), x3)) -> c10(A__PLUS(a__U12(s(mark(z0)), x1, x2), mark(x3)), MARK(U12(s(z0), x1, x2))) MARK(plus(U12(x0, x1, x2), tt)) -> c10(MARK(U12(x0, x1, x2))) MARK(plus(U12(0, x1, x2), x3)) -> c10(A__PLUS(a__U12(0, x1, x2), mark(x3))) MARK(plus(plus(x0, x1), s(z0))) -> c10(A__PLUS(a__plus(mark(x0), mark(x1)), s(mark(z0))), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), 0)) -> c10(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c10(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, U11(z0, z1, z2)), x2)) -> c10(A__PLUS(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), mark(x2)), MARK(plus(x0, U11(z0, z1, z2)))) MARK(plus(plus(x0, U12(z0, z1, z2)), x2)) -> c10(A__PLUS(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), mark(x2)), MARK(plus(x0, U12(z0, z1, z2)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c10(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)) -> c10(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, s(z0)), x2)) -> c10(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(x0, 0), x2)) -> c10(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(U11(z0, z1, z2), x1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(plus(U11(z0, z1, z2), x1))) MARK(plus(plus(U12(z0, z1, z2), x1), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(plus(U12(z0, z1, z2), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c10(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)) -> c10(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(0, x1), x2)) -> c10(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(x0, x1), tt)) -> c10(MARK(plus(x0, x1))) MARK(plus(s(x0), s(z0))) -> c10(A__PLUS(s(mark(x0)), s(mark(z0))), MARK(s(x0))) MARK(plus(s(x0), 0)) -> c10(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(U11(z0, z1, z2)), x1)) -> c10(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x1)), MARK(s(U11(z0, z1, z2)))) MARK(plus(s(U12(z0, z1, z2)), x1)) -> c10(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x1)), MARK(s(U12(z0, z1, z2)))) MARK(plus(s(plus(z0, z1)), x1)) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c10(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(s(z0)), x1)) -> c10(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(0), x1)) -> c10(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(x0), x1)) -> c10(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c10(MARK(s(x0))) MARK(plus(tt, s(z0))) -> c10(A__PLUS(tt, s(mark(z0)))) MARK(plus(tt, 0)) -> c10(A__PLUS(tt, 0)) MARK(plus(0, s(z0))) -> c10(A__PLUS(0, s(mark(z0)))) MARK(plus(0, 0)) -> c10(A__PLUS(0, 0)) MARK(plus(x0, U11(U11(z0, z1, z2), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(a__U11(mark(z0), z1, z2), x2, x3)), MARK(U11(U11(z0, z1, z2), x2, x3))) MARK(plus(x0, U11(U12(z0, z1, z2), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(a__U12(mark(z0), z1, z2), x2, x3)), MARK(U11(U12(z0, z1, z2), x2, x3))) MARK(plus(x0, U11(plus(z0, z1), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(U11(plus(z0, z1), x2, x3))) MARK(plus(x0, U11(tt, x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(tt, x2, x3)), MARK(U11(tt, x2, x3))) MARK(plus(x0, U11(s(z0), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(s(mark(z0)), x2, x3)), MARK(U11(s(z0), x2, x3))) MARK(plus(U11(z0, z1, z2), U11(x1, x2, x3))) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(U12(z0, z1, z2), U11(x1, x2, x3))) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(plus(z0, z1), U11(x1, x2, x3))) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(tt, U11(x1, x2, x3))) -> c11(A__PLUS(tt, a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(s(z0), U11(x1, x2, x3))) -> c11(A__PLUS(s(mark(z0)), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(0, U11(x1, x2, x3))) -> c11(A__PLUS(0, a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(x0, U11(x1, z1, z2))) -> c11(MARK(U11(x1, z1, z2))) MARK(plus(x0, U11(0, x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(0, x2, x3))) MARK(plus(x0, U12(U11(z0, z1, z2), x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(a__U11(mark(z0), z1, z2), x2, x3)), MARK(U12(U11(z0, z1, z2), x2, x3))) MARK(plus(x0, U12(U12(z0, z1, z2), x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(a__U12(mark(z0), z1, z2), x2, x3)), MARK(U12(U12(z0, z1, z2), x2, x3))) MARK(plus(x0, U12(plus(z0, z1), x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(U12(plus(z0, z1), x2, x3))) MARK(plus(x0, U12(tt, x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(tt, x2, x3)), MARK(U12(tt, x2, x3))) MARK(plus(x0, U12(s(z0), x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(s(mark(z0)), x2, x3)), MARK(U12(s(z0), x2, x3))) MARK(plus(U11(z0, z1, z2), U12(x1, x2, x3))) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(U12(z0, z1, z2), U12(x1, x2, x3))) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(plus(z0, z1), U12(x1, x2, x3))) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(tt, U12(x1, x2, x3))) -> c11(A__PLUS(tt, a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(s(z0), U12(x1, x2, x3))) -> c11(A__PLUS(s(mark(z0)), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(0, U12(x1, x2, x3))) -> c11(A__PLUS(0, a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(x0, U12(x1, z1, z2))) -> c11(MARK(U12(x1, z1, z2))) MARK(plus(x0, U12(0, x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(0, x2, x3))) MARK(plus(x0, plus(x1, U11(z0, z1, z2)))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), a__U11(mark(z0), z1, z2))), MARK(plus(x1, U11(z0, z1, z2)))) MARK(plus(x0, plus(x1, U12(z0, z1, z2)))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), a__U12(mark(z0), z1, z2))), MARK(plus(x1, U12(z0, z1, z2)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c11(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))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, s(z0)))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(x1, 0))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(U11(z0, z1, z2), x2))) -> c11(A__PLUS(mark(x0), a__plus(a__U11(mark(z0), z1, z2), mark(x2))), MARK(plus(U11(z0, z1, z2), x2))) MARK(plus(x0, plus(U12(z0, z1, z2), x2))) -> c11(A__PLUS(mark(x0), a__plus(a__U12(mark(z0), z1, z2), mark(x2))), MARK(plus(U12(z0, z1, z2), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c11(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))) -> c11(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c11(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(x0, plus(0, x2))) -> c11(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(U11(z0, z1, z2), plus(x1, x2))) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(U12(z0, z1, z2), plus(x1, x2))) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c11(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c11(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c11(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c11(MARK(plus(x1, x2))) MARK(plus(U11(x0, x1, x2), s(z0))) -> c11(A__PLUS(a__U11(mark(x0), x1, x2), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(x0, z1, z2), x3)) -> c11(A__PLUS(U11(mark(x0), z1, z2), mark(x3)), MARK(x3)) MARK(plus(U11(U11(z0, z1, z2), x1, x2), x3)) -> c11(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(U12(z0, z1, z2), x1, x2), x3)) -> c11(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(plus(z0, z1), x1, x2), x3)) -> c11(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(tt, x1, x2), x3)) -> c11(A__PLUS(a__U11(tt, x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(s(z0), x1, x2), x3)) -> c11(A__PLUS(a__U11(s(mark(z0)), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(0, x1, x2), x3)) -> c11(A__PLUS(a__U11(0, x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(x0, x1, x2), 0)) -> c11(A__PLUS(a__U11(mark(x0), x1, x2), 0)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U12(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c3(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c3(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U12(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U12(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U12(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, 0) -> c3(A__PLUS(0, 0)) MARK(U11(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U11(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U11(U11(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U11(U11(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U11(U11(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U11(U11(x0, z1, z2), x3, x4)) -> c8(MARK(U11(x0, z1, z2))) MARK(U11(U11(0, x1, x2), x3, x4)) -> c8(A__U11(a__U11(0, x1, x2), x3, x4)) MARK(U11(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U11(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U11(U12(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U11(U12(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U11(U12(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U11(U12(x0, z1, z2), x3, x4)) -> c8(MARK(U12(x0, z1, z2))) MARK(U11(U12(0, x1, x2), x3, x4)) -> c8(A__U11(a__U12(0, x1, x2), x3, x4)) MARK(U11(plus(x0, U11(z0, z1, z2)), x2, x3)) -> 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c10(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(plus(U12(plus(z0, z1), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(U12(plus(z0, z1), x1, x2))) MARK(plus(U12(tt, x1, x2), x3)) -> c10(A__PLUS(a__U12(tt, x1, x2), mark(x3)), MARK(U12(tt, x1, x2))) MARK(plus(U12(s(z0), x1, x2), x3)) -> c10(A__PLUS(a__U12(s(mark(z0)), x1, x2), mark(x3)), MARK(U12(s(z0), x1, x2))) MARK(plus(U12(x0, x1, x2), tt)) -> c10(MARK(U12(x0, x1, x2))) MARK(plus(U12(0, x1, x2), x3)) -> c10(A__PLUS(a__U12(0, x1, x2), mark(x3))) MARK(plus(plus(x0, x1), s(z0))) -> c10(A__PLUS(a__plus(mark(x0), mark(x1)), s(mark(z0))), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), 0)) -> c10(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c10(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, U11(z0, z1, z2)), x2)) -> c10(A__PLUS(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), mark(x2)), MARK(plus(x0, U11(z0, z1, z2)))) MARK(plus(plus(x0, U12(z0, z1, z2)), x2)) -> c10(A__PLUS(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), mark(x2)), MARK(plus(x0, U12(z0, z1, z2)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c10(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)) -> c10(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, s(z0)), x2)) -> c10(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(x0, 0), x2)) -> c10(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(U11(z0, z1, z2), x1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(plus(U11(z0, z1, z2), x1))) MARK(plus(plus(U12(z0, z1, z2), x1), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(plus(U12(z0, z1, z2), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c10(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)) -> c10(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(0, x1), x2)) -> c10(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(x0, x1), tt)) -> c10(MARK(plus(x0, x1))) MARK(plus(s(x0), s(z0))) -> c10(A__PLUS(s(mark(x0)), s(mark(z0))), MARK(s(x0))) MARK(plus(s(x0), 0)) -> c10(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(U11(z0, z1, z2)), x1)) -> c10(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x1)), MARK(s(U11(z0, z1, z2)))) MARK(plus(s(U12(z0, z1, z2)), x1)) -> c10(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x1)), MARK(s(U12(z0, z1, z2)))) MARK(plus(s(plus(z0, z1)), x1)) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c10(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(s(z0)), x1)) -> c10(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(0), x1)) -> c10(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(x0), x1)) -> c10(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c10(MARK(s(x0))) MARK(plus(tt, s(z0))) -> c10(A__PLUS(tt, s(mark(z0)))) MARK(plus(tt, 0)) -> c10(A__PLUS(tt, 0)) MARK(plus(0, s(z0))) -> c10(A__PLUS(0, s(mark(z0)))) MARK(plus(0, 0)) -> c10(A__PLUS(0, 0)) MARK(plus(x0, U11(U11(z0, z1, z2), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(a__U11(mark(z0), z1, z2), x2, x3)), MARK(U11(U11(z0, z1, z2), x2, x3))) MARK(plus(x0, U11(U12(z0, z1, z2), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(a__U12(mark(z0), z1, z2), x2, x3)), MARK(U11(U12(z0, z1, z2), x2, x3))) MARK(plus(x0, U11(plus(z0, z1), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(U11(plus(z0, z1), x2, x3))) MARK(plus(x0, U11(tt, x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(tt, x2, x3)), MARK(U11(tt, x2, x3))) MARK(plus(x0, U11(s(z0), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(s(mark(z0)), x2, x3)), MARK(U11(s(z0), x2, x3))) MARK(plus(U11(z0, z1, z2), U11(x1, x2, x3))) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(U12(z0, z1, z2), U11(x1, x2, x3))) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(plus(z0, z1), U11(x1, x2, x3))) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(tt, U11(x1, x2, x3))) -> c11(A__PLUS(tt, a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(s(z0), U11(x1, x2, x3))) -> c11(A__PLUS(s(mark(z0)), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(0, U11(x1, x2, x3))) -> c11(A__PLUS(0, a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(x0, U11(x1, z1, z2))) -> c11(MARK(U11(x1, z1, z2))) MARK(plus(x0, U11(0, x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(0, x2, x3))) MARK(plus(x0, U12(U11(z0, z1, z2), x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(a__U11(mark(z0), z1, z2), x2, x3)), MARK(U12(U11(z0, z1, z2), x2, x3))) MARK(plus(x0, U12(U12(z0, z1, z2), x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(a__U12(mark(z0), z1, z2), x2, x3)), MARK(U12(U12(z0, z1, z2), x2, x3))) MARK(plus(x0, U12(plus(z0, z1), x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(U12(plus(z0, z1), x2, x3))) MARK(plus(x0, U12(tt, x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(tt, x2, x3)), MARK(U12(tt, x2, x3))) MARK(plus(x0, U12(s(z0), x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(s(mark(z0)), x2, x3)), MARK(U12(s(z0), x2, x3))) MARK(plus(U11(z0, z1, z2), U12(x1, x2, x3))) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(U12(z0, z1, z2), U12(x1, x2, x3))) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(plus(z0, z1), U12(x1, x2, x3))) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(tt, U12(x1, x2, x3))) -> c11(A__PLUS(tt, a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(s(z0), U12(x1, x2, x3))) -> c11(A__PLUS(s(mark(z0)), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(0, U12(x1, x2, x3))) -> c11(A__PLUS(0, a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(x0, U12(x1, z1, z2))) -> c11(MARK(U12(x1, z1, z2))) MARK(plus(x0, U12(0, x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(0, x2, x3))) MARK(plus(x0, plus(x1, U11(z0, z1, z2)))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), a__U11(mark(z0), z1, z2))), MARK(plus(x1, U11(z0, z1, z2)))) MARK(plus(x0, plus(x1, U12(z0, z1, z2)))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), a__U12(mark(z0), z1, z2))), MARK(plus(x1, U12(z0, z1, z2)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c11(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))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, s(z0)))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(x1, 0))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(U11(z0, z1, z2), x2))) -> c11(A__PLUS(mark(x0), a__plus(a__U11(mark(z0), z1, z2), mark(x2))), MARK(plus(U11(z0, z1, z2), x2))) MARK(plus(x0, plus(U12(z0, z1, z2), x2))) -> c11(A__PLUS(mark(x0), a__plus(a__U12(mark(z0), z1, z2), mark(x2))), MARK(plus(U12(z0, z1, z2), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c11(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))) -> c11(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c11(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(x0, plus(0, x2))) -> c11(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(U11(z0, z1, z2), plus(x1, x2))) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(U12(z0, z1, z2), plus(x1, x2))) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c11(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c11(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c11(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c11(MARK(plus(x1, x2))) MARK(plus(U11(x0, x1, x2), s(z0))) -> c11(A__PLUS(a__U11(mark(x0), x1, x2), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(x0, z1, z2), x3)) -> c11(A__PLUS(U11(mark(x0), z1, z2), mark(x3)), MARK(x3)) MARK(plus(U11(U11(z0, z1, z2), x1, x2), x3)) -> c11(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(U12(z0, z1, z2), x1, x2), x3)) -> c11(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(plus(z0, z1), x1, x2), x3)) -> c11(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(tt, x1, x2), x3)) -> c11(A__PLUS(a__U11(tt, x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(s(z0), x1, x2), x3)) -> c11(A__PLUS(a__U11(s(mark(z0)), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(0, x1, x2), x3)) -> c11(A__PLUS(a__U11(0, x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(x0, x1, x2), 0)) -> c11(A__PLUS(a__U11(mark(x0), x1, x2), 0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_1, c9_1, c10_2, c10_1, c11_2, c11_1, c8_2, c9_2 ---------------------------------------- (219) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(U12(z0, z1, z2), x1)) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) by MARK(plus(U12(x0, x1, x2), U11(z0, z1, z2))) -> c11(A__PLUS(a__U12(mark(x0), x1, x2), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(U12(x0, x1, x2), U12(z0, z1, z2))) -> c11(A__PLUS(a__U12(mark(x0), x1, x2), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(U12(x0, x1, x2), plus(z0, z1))) -> c11(A__PLUS(a__U12(mark(x0), x1, x2), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(U12(x0, x1, x2), tt)) -> c11(A__PLUS(a__U12(mark(x0), x1, x2), tt), MARK(tt)) MARK(plus(U12(x0, x1, x2), s(z0))) -> c11(A__PLUS(a__U12(mark(x0), x1, x2), s(mark(z0))), MARK(s(z0))) MARK(plus(U12(x0, x1, x2), 0)) -> c11(A__PLUS(a__U12(mark(x0), x1, x2), 0), MARK(0)) MARK(plus(U12(x0, z1, z2), x3)) -> c11(A__PLUS(U12(mark(x0), z1, z2), mark(x3)), MARK(x3)) MARK(plus(U12(U11(z0, z1, z2), x1, x2), x3)) -> c11(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(U12(z0, z1, z2), x1, x2), x3)) -> c11(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(plus(z0, z1), x1, x2), x3)) -> c11(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(tt, x1, x2), x3)) -> c11(A__PLUS(a__U12(tt, x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(s(z0), x1, x2), x3)) -> c11(A__PLUS(a__U12(s(mark(z0)), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(0, x1, x2), x3)) -> c11(A__PLUS(a__U12(0, x1, x2), mark(x3)), MARK(x3)) ---------------------------------------- (220) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U12(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c3(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c3(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U12(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U12(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U12(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, 0) -> c3(A__PLUS(0, 0)) MARK(U11(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U11(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U11(U11(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U11(U11(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U11(U11(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U11(U11(x0, z1, z2), x3, x4)) -> c8(MARK(U11(x0, z1, z2))) MARK(U11(U11(0, x1, x2), x3, x4)) -> c8(A__U11(a__U11(0, x1, x2), x3, x4)) MARK(U11(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U11(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U11(U12(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U11(U12(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U11(U12(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U11(U12(x0, z1, z2), 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-> c10(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, U11(z0, z1, z2)), x2)) -> c10(A__PLUS(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), mark(x2)), MARK(plus(x0, U11(z0, z1, z2)))) MARK(plus(plus(x0, U12(z0, z1, z2)), x2)) -> c10(A__PLUS(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), mark(x2)), MARK(plus(x0, U12(z0, z1, z2)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c10(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)) -> c10(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, s(z0)), x2)) -> c10(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(x0, 0), x2)) -> c10(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(U11(z0, z1, z2), x1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(plus(U11(z0, z1, z2), x1))) MARK(plus(plus(U12(z0, z1, z2), x1), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(plus(U12(z0, z1, z2), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c10(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)) -> c10(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(0, x1), x2)) -> c10(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(x0, x1), tt)) -> c10(MARK(plus(x0, x1))) MARK(plus(s(x0), s(z0))) -> c10(A__PLUS(s(mark(x0)), s(mark(z0))), MARK(s(x0))) MARK(plus(s(x0), 0)) -> c10(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(U11(z0, z1, z2)), x1)) -> c10(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x1)), MARK(s(U11(z0, z1, z2)))) MARK(plus(s(U12(z0, z1, z2)), x1)) -> c10(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x1)), MARK(s(U12(z0, z1, z2)))) MARK(plus(s(plus(z0, z1)), x1)) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c10(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(s(z0)), x1)) -> c10(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(0), x1)) -> c10(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(x0), x1)) -> c10(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c10(MARK(s(x0))) MARK(plus(tt, s(z0))) -> c10(A__PLUS(tt, s(mark(z0)))) MARK(plus(tt, 0)) -> c10(A__PLUS(tt, 0)) MARK(plus(0, s(z0))) -> c10(A__PLUS(0, s(mark(z0)))) MARK(plus(0, 0)) -> c10(A__PLUS(0, 0)) MARK(plus(x0, U11(U11(z0, z1, z2), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(a__U11(mark(z0), z1, z2), x2, x3)), MARK(U11(U11(z0, z1, z2), x2, x3))) MARK(plus(x0, U11(U12(z0, z1, z2), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(a__U12(mark(z0), z1, z2), x2, x3)), MARK(U11(U12(z0, z1, z2), x2, x3))) MARK(plus(x0, U11(plus(z0, z1), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(U11(plus(z0, z1), x2, x3))) MARK(plus(x0, U11(tt, x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(tt, x2, x3)), MARK(U11(tt, x2, x3))) MARK(plus(x0, U11(s(z0), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(s(mark(z0)), x2, x3)), MARK(U11(s(z0), x2, x3))) MARK(plus(U11(z0, z1, z2), U11(x1, x2, x3))) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(U12(z0, z1, z2), U11(x1, x2, x3))) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(plus(z0, z1), U11(x1, x2, x3))) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(tt, U11(x1, x2, x3))) -> c11(A__PLUS(tt, a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(s(z0), U11(x1, x2, x3))) -> c11(A__PLUS(s(mark(z0)), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(0, U11(x1, x2, x3))) -> c11(A__PLUS(0, a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(x0, U11(x1, z1, z2))) -> c11(MARK(U11(x1, z1, z2))) MARK(plus(x0, U11(0, x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(0, x2, x3))) MARK(plus(x0, U12(U11(z0, z1, z2), x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(a__U11(mark(z0), z1, z2), x2, x3)), MARK(U12(U11(z0, z1, z2), x2, x3))) MARK(plus(x0, U12(U12(z0, z1, z2), x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(a__U12(mark(z0), z1, z2), x2, x3)), MARK(U12(U12(z0, z1, z2), x2, x3))) MARK(plus(x0, U12(plus(z0, z1), x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(U12(plus(z0, z1), x2, x3))) MARK(plus(x0, U12(tt, x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(tt, x2, x3)), MARK(U12(tt, x2, x3))) MARK(plus(x0, U12(s(z0), x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(s(mark(z0)), x2, x3)), MARK(U12(s(z0), x2, x3))) MARK(plus(U11(z0, z1, z2), U12(x1, x2, x3))) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(U12(z0, z1, z2), U12(x1, x2, x3))) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(plus(z0, z1), U12(x1, x2, x3))) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(tt, U12(x1, x2, x3))) -> c11(A__PLUS(tt, a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(s(z0), U12(x1, x2, x3))) -> c11(A__PLUS(s(mark(z0)), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(0, U12(x1, x2, x3))) -> c11(A__PLUS(0, a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(x0, U12(x1, z1, z2))) -> c11(MARK(U12(x1, z1, z2))) MARK(plus(x0, U12(0, x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(0, x2, x3))) MARK(plus(x0, plus(x1, U11(z0, z1, z2)))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), a__U11(mark(z0), z1, z2))), MARK(plus(x1, U11(z0, z1, z2)))) MARK(plus(x0, plus(x1, U12(z0, z1, z2)))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), a__U12(mark(z0), z1, z2))), MARK(plus(x1, U12(z0, z1, z2)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c11(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))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, s(z0)))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(x1, 0))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(U11(z0, z1, z2), x2))) -> c11(A__PLUS(mark(x0), a__plus(a__U11(mark(z0), z1, z2), mark(x2))), MARK(plus(U11(z0, z1, z2), x2))) MARK(plus(x0, plus(U12(z0, z1, z2), x2))) -> c11(A__PLUS(mark(x0), a__plus(a__U12(mark(z0), z1, z2), mark(x2))), MARK(plus(U12(z0, z1, z2), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c11(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))) -> c11(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c11(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(x0, plus(0, x2))) -> c11(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(U11(z0, z1, z2), plus(x1, x2))) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(U12(z0, z1, z2), plus(x1, x2))) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c11(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c11(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c11(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c11(MARK(plus(x1, x2))) MARK(plus(U11(x0, x1, x2), s(z0))) -> c11(A__PLUS(a__U11(mark(x0), x1, x2), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(x0, z1, z2), x3)) -> c11(A__PLUS(U11(mark(x0), z1, z2), mark(x3)), MARK(x3)) MARK(plus(U11(U11(z0, z1, z2), x1, x2), x3)) -> c11(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(U12(z0, z1, z2), x1, x2), x3)) -> c11(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(plus(z0, z1), x1, x2), x3)) -> c11(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(tt, x1, x2), x3)) -> c11(A__PLUS(a__U11(tt, x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(s(z0), x1, x2), x3)) -> c11(A__PLUS(a__U11(s(mark(z0)), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(0, x1, x2), x3)) -> c11(A__PLUS(a__U11(0, x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(x0, x1, x2), 0)) -> c11(A__PLUS(a__U11(mark(x0), x1, x2), 0)) MARK(plus(U12(x0, x1, x2), tt)) -> c11(A__PLUS(a__U12(mark(x0), x1, x2), tt), MARK(tt)) MARK(plus(U12(x0, x1, x2), s(z0))) -> c11(A__PLUS(a__U12(mark(x0), x1, x2), s(mark(z0))), MARK(s(z0))) MARK(plus(U12(x0, x1, x2), 0)) -> c11(A__PLUS(a__U12(mark(x0), x1, x2), 0), MARK(0)) MARK(plus(U12(x0, z1, z2), x3)) -> c11(A__PLUS(U12(mark(x0), z1, z2), mark(x3)), MARK(x3)) MARK(plus(U12(U11(z0, z1, z2), x1, x2), x3)) -> c11(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(U12(z0, z1, z2), x1, x2), x3)) -> c11(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(plus(z0, z1), x1, x2), x3)) -> c11(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(tt, x1, x2), x3)) -> c11(A__PLUS(a__U12(tt, x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(s(z0), x1, x2), x3)) -> c11(A__PLUS(a__U12(s(mark(z0)), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(0, x1, x2), x3)) -> c11(A__PLUS(a__U12(0, x1, x2), mark(x3)), MARK(x3)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, 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x3))) -> c11(A__PLUS(mark(x0), a__U12(a__U12(mark(z0), z1, z2), x2, x3)), MARK(U12(U12(z0, z1, z2), x2, x3))) MARK(plus(x0, U12(plus(z0, z1), x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(U12(plus(z0, z1), x2, x3))) MARK(plus(x0, U12(tt, x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(tt, x2, x3)), MARK(U12(tt, x2, x3))) MARK(plus(x0, U12(s(z0), x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(s(mark(z0)), x2, x3)), MARK(U12(s(z0), x2, x3))) MARK(plus(U11(z0, z1, z2), U12(x1, x2, x3))) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(U12(z0, z1, z2), U12(x1, x2, x3))) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(plus(z0, z1), U12(x1, x2, x3))) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(tt, U12(x1, x2, x3))) -> c11(A__PLUS(tt, a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(s(z0), U12(x1, x2, x3))) -> c11(A__PLUS(s(mark(z0)), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(0, U12(x1, x2, x3))) -> c11(A__PLUS(0, a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(x0, U12(x1, z1, z2))) -> c11(MARK(U12(x1, z1, z2))) MARK(plus(x0, U12(0, x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(0, x2, x3))) MARK(plus(x0, plus(x1, U11(z0, z1, z2)))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), a__U11(mark(z0), z1, z2))), MARK(plus(x1, U11(z0, z1, z2)))) MARK(plus(x0, plus(x1, U12(z0, z1, z2)))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), a__U12(mark(z0), z1, z2))), MARK(plus(x1, U12(z0, z1, z2)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c11(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))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, s(z0)))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(x1, 0))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(U11(z0, z1, z2), x2))) -> c11(A__PLUS(mark(x0), a__plus(a__U11(mark(z0), z1, z2), mark(x2))), MARK(plus(U11(z0, z1, z2), x2))) MARK(plus(x0, plus(U12(z0, z1, z2), x2))) -> c11(A__PLUS(mark(x0), a__plus(a__U12(mark(z0), z1, z2), mark(x2))), MARK(plus(U12(z0, z1, z2), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c11(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))) -> c11(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c11(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(x0, plus(0, x2))) -> c11(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(U11(z0, z1, z2), plus(x1, x2))) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(U12(z0, z1, z2), plus(x1, x2))) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c11(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c11(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c11(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c11(MARK(plus(x1, x2))) MARK(plus(U11(x0, x1, x2), s(z0))) -> c11(A__PLUS(a__U11(mark(x0), x1, x2), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(x0, z1, z2), x3)) -> c11(A__PLUS(U11(mark(x0), z1, z2), mark(x3)), MARK(x3)) MARK(plus(U11(U11(z0, z1, z2), x1, x2), x3)) -> c11(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(U12(z0, z1, z2), x1, x2), x3)) -> c11(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(plus(z0, z1), x1, x2), x3)) -> c11(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(tt, x1, x2), x3)) -> c11(A__PLUS(a__U11(tt, x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(s(z0), x1, x2), x3)) -> c11(A__PLUS(a__U11(s(mark(z0)), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(0, x1, x2), x3)) -> c11(A__PLUS(a__U11(0, x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(x0, x1, x2), 0)) -> c11(A__PLUS(a__U11(mark(x0), x1, x2), 0)) MARK(plus(U12(x0, x1, x2), tt)) -> c11(A__PLUS(a__U12(mark(x0), x1, x2), tt), MARK(tt)) MARK(plus(U12(x0, x1, x2), s(z0))) -> c11(A__PLUS(a__U12(mark(x0), x1, x2), s(mark(z0))), MARK(s(z0))) MARK(plus(U12(x0, x1, x2), 0)) -> c11(A__PLUS(a__U12(mark(x0), x1, x2), 0), MARK(0)) MARK(plus(U12(x0, z1, z2), x3)) -> c11(A__PLUS(U12(mark(x0), z1, z2), mark(x3)), MARK(x3)) MARK(plus(U12(U11(z0, z1, z2), x1, x2), x3)) -> c11(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(U12(z0, z1, z2), x1, x2), x3)) -> c11(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(plus(z0, z1), x1, x2), x3)) -> c11(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(tt, x1, x2), x3)) -> c11(A__PLUS(a__U12(tt, x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(s(z0), x1, x2), x3)) -> c11(A__PLUS(a__U12(s(mark(z0)), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(0, x1, x2), x3)) -> c11(A__PLUS(a__U12(0, x1, x2), mark(x3)), MARK(x3)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_1, c9_1, c10_2, c10_1, c11_2, c11_1, c8_2, c9_2 ---------------------------------------- (221) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(plus(U12(x0, x1, x2), tt)) -> c11(A__PLUS(a__U12(mark(x0), x1, x2), tt), MARK(tt)) ---------------------------------------- (222) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, 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U12(0, x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(0, x2, x3))) MARK(plus(x0, plus(x1, U11(z0, z1, z2)))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), a__U11(mark(z0), z1, z2))), MARK(plus(x1, U11(z0, z1, z2)))) MARK(plus(x0, plus(x1, U12(z0, z1, z2)))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), a__U12(mark(z0), z1, z2))), MARK(plus(x1, U12(z0, z1, z2)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c11(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))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, s(z0)))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(x1, 0))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(U11(z0, z1, z2), x2))) -> c11(A__PLUS(mark(x0), a__plus(a__U11(mark(z0), z1, z2), mark(x2))), MARK(plus(U11(z0, z1, z2), x2))) MARK(plus(x0, plus(U12(z0, z1, z2), x2))) -> c11(A__PLUS(mark(x0), a__plus(a__U12(mark(z0), z1, z2), mark(x2))), MARK(plus(U12(z0, z1, z2), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c11(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))) -> c11(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c11(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(x0, plus(0, x2))) -> c11(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(U11(z0, z1, z2), plus(x1, x2))) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(U12(z0, z1, z2), plus(x1, x2))) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c11(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c11(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c11(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c11(MARK(plus(x1, x2))) MARK(plus(U11(x0, x1, x2), s(z0))) -> c11(A__PLUS(a__U11(mark(x0), x1, x2), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(x0, z1, z2), x3)) -> c11(A__PLUS(U11(mark(x0), z1, z2), mark(x3)), MARK(x3)) MARK(plus(U11(U11(z0, z1, z2), x1, x2), x3)) -> c11(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(U12(z0, z1, z2), x1, x2), x3)) -> c11(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(plus(z0, z1), x1, x2), x3)) -> c11(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(tt, x1, x2), x3)) -> c11(A__PLUS(a__U11(tt, x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(s(z0), x1, x2), x3)) -> c11(A__PLUS(a__U11(s(mark(z0)), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(0, x1, x2), x3)) -> c11(A__PLUS(a__U11(0, x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(x0, x1, x2), 0)) -> c11(A__PLUS(a__U11(mark(x0), x1, x2), 0)) MARK(plus(U12(x0, x1, x2), s(z0))) -> c11(A__PLUS(a__U12(mark(x0), x1, x2), s(mark(z0))), MARK(s(z0))) MARK(plus(U12(x0, x1, x2), 0)) -> c11(A__PLUS(a__U12(mark(x0), x1, x2), 0), MARK(0)) MARK(plus(U12(x0, z1, z2), x3)) -> c11(A__PLUS(U12(mark(x0), z1, z2), mark(x3)), MARK(x3)) MARK(plus(U12(U11(z0, z1, z2), x1, x2), x3)) -> c11(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(U12(z0, z1, z2), x1, x2), x3)) -> c11(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(plus(z0, z1), x1, x2), x3)) -> c11(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(tt, x1, x2), x3)) -> c11(A__PLUS(a__U12(tt, x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(s(z0), x1, x2), x3)) -> c11(A__PLUS(a__U12(s(mark(z0)), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(0, x1, x2), x3)) -> c11(A__PLUS(a__U12(0, x1, x2), mark(x3)), MARK(x3)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) 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x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), 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z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, 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c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U12(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(s(z0), U12(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(x0, U12(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U12(x1, x2, x3))) -> c10(A__PLUS(tt, a__U12(mark(x1), x2, x3))) MARK(plus(0, U12(x1, x2, x3))) -> c10(A__PLUS(0, a__U12(mark(x1), x2, x3))) MARK(plus(x0, plus(x1, U11(z0, z1, z2)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__U11(mark(z0), z1, z2))), MARK(x0)) MARK(plus(x0, plus(x1, U12(z0, z1, z2)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__U12(mark(z0), z1, z2))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c10(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, 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c10(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c10(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))) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c10(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c10(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c10(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(U11(x0, x1, x2), s(z0))) -> c10(A__PLUS(a__U11(mark(x0), x1, x2), s(mark(z0))), MARK(U11(x0, x1, x2))) MARK(plus(U11(x0, x1, x2), 0)) -> c10(A__PLUS(a__U11(mark(x0), x1, x2), 0), MARK(U11(x0, x1, x2))) MARK(plus(U11(x0, z1, z2), x3)) -> c10(A__PLUS(U11(mark(x0), z1, z2), mark(x3)), MARK(U11(x0, z1, z2))) MARK(plus(U11(U11(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(plus(U11(U12(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(plus(U11(plus(z0, z1), x1, x2), x3)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(U11(plus(z0, z1), x1, x2))) MARK(plus(U11(tt, x1, x2), x3)) -> c10(A__PLUS(a__U11(tt, x1, x2), mark(x3)), MARK(U11(tt, x1, x2))) MARK(plus(U11(s(z0), x1, x2), x3)) -> c10(A__PLUS(a__U11(s(mark(z0)), x1, x2), mark(x3)), MARK(U11(s(z0), x1, x2))) MARK(plus(U11(x0, x1, x2), tt)) -> c10(MARK(U11(x0, x1, x2))) MARK(plus(U11(0, x1, x2), x3)) -> c10(A__PLUS(a__U11(0, x1, x2), mark(x3))) MARK(plus(U12(x0, x1, x2), s(z0))) -> c10(A__PLUS(a__U12(mark(x0), x1, x2), s(mark(z0))), MARK(U12(x0, x1, x2))) MARK(plus(U12(x0, x1, x2), 0)) -> c10(A__PLUS(a__U12(mark(x0), x1, x2), 0), MARK(U12(x0, x1, x2))) MARK(plus(U12(x0, z1, z2), x3)) -> c10(A__PLUS(U12(mark(x0), z1, z2), mark(x3)), MARK(U12(x0, z1, z2))) MARK(plus(U12(U11(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(plus(U12(U12(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(plus(U12(plus(z0, z1), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(U12(plus(z0, z1), x1, x2))) MARK(plus(U12(tt, x1, x2), x3)) -> c10(A__PLUS(a__U12(tt, x1, x2), mark(x3)), MARK(U12(tt, x1, x2))) MARK(plus(U12(s(z0), x1, x2), x3)) -> c10(A__PLUS(a__U12(s(mark(z0)), x1, x2), mark(x3)), MARK(U12(s(z0), x1, x2))) MARK(plus(U12(x0, x1, x2), tt)) -> c10(MARK(U12(x0, x1, x2))) MARK(plus(U12(0, x1, x2), x3)) -> c10(A__PLUS(a__U12(0, x1, x2), mark(x3))) MARK(plus(plus(x0, x1), s(z0))) -> c10(A__PLUS(a__plus(mark(x0), mark(x1)), s(mark(z0))), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), 0)) -> c10(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) 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MARK(plus(s(plus(z0, z1)), x1)) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c10(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(s(z0)), x1)) -> c10(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(0), x1)) -> c10(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(x0), x1)) -> c10(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c10(MARK(s(x0))) MARK(plus(tt, s(z0))) -> c10(A__PLUS(tt, s(mark(z0)))) MARK(plus(tt, 0)) -> c10(A__PLUS(tt, 0)) MARK(plus(0, s(z0))) -> c10(A__PLUS(0, s(mark(z0)))) MARK(plus(0, 0)) -> c10(A__PLUS(0, 0)) MARK(plus(x0, U11(U11(z0, z1, z2), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(a__U11(mark(z0), z1, z2), x2, x3)), MARK(U11(U11(z0, z1, z2), x2, x3))) MARK(plus(x0, U11(U12(z0, z1, z2), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(a__U12(mark(z0), z1, z2), x2, x3)), MARK(U11(U12(z0, z1, z2), x2, x3))) MARK(plus(x0, U11(plus(z0, z1), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(U11(plus(z0, z1), x2, x3))) MARK(plus(x0, U11(tt, x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(tt, x2, x3)), MARK(U11(tt, x2, x3))) MARK(plus(x0, U11(s(z0), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(s(mark(z0)), x2, x3)), MARK(U11(s(z0), x2, x3))) MARK(plus(U11(z0, z1, z2), U11(x1, x2, x3))) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(U12(z0, z1, z2), U11(x1, x2, x3))) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(plus(z0, z1), U11(x1, x2, x3))) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(tt, U11(x1, x2, x3))) -> c11(A__PLUS(tt, a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(s(z0), U11(x1, x2, x3))) -> c11(A__PLUS(s(mark(z0)), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(0, U11(x1, x2, x3))) -> c11(A__PLUS(0, a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(x0, U11(x1, z1, z2))) -> c11(MARK(U11(x1, z1, z2))) MARK(plus(x0, U11(0, x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(0, x2, x3))) MARK(plus(x0, U12(U11(z0, z1, z2), x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(a__U11(mark(z0), z1, z2), x2, x3)), MARK(U12(U11(z0, z1, z2), x2, x3))) MARK(plus(x0, U12(U12(z0, z1, z2), x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(a__U12(mark(z0), z1, z2), x2, x3)), MARK(U12(U12(z0, z1, z2), x2, x3))) MARK(plus(x0, U12(plus(z0, z1), x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(U12(plus(z0, z1), x2, x3))) MARK(plus(x0, U12(tt, x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(tt, x2, x3)), MARK(U12(tt, x2, x3))) MARK(plus(x0, U12(s(z0), x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(s(mark(z0)), x2, x3)), MARK(U12(s(z0), x2, x3))) MARK(plus(U11(z0, z1, z2), U12(x1, x2, x3))) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(U12(z0, z1, z2), U12(x1, x2, x3))) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(plus(z0, z1), U12(x1, x2, x3))) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(tt, U12(x1, x2, x3))) -> c11(A__PLUS(tt, a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(s(z0), U12(x1, x2, x3))) -> c11(A__PLUS(s(mark(z0)), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(0, U12(x1, x2, x3))) -> c11(A__PLUS(0, a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(x0, U12(x1, z1, z2))) -> c11(MARK(U12(x1, z1, z2))) MARK(plus(x0, U12(0, x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(0, x2, x3))) MARK(plus(x0, plus(x1, U11(z0, z1, z2)))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), a__U11(mark(z0), z1, z2))), MARK(plus(x1, U11(z0, z1, z2)))) MARK(plus(x0, plus(x1, U12(z0, z1, z2)))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), a__U12(mark(z0), z1, z2))), MARK(plus(x1, U12(z0, z1, z2)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c11(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))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, s(z0)))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(x1, 0))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(U11(z0, z1, z2), x2))) -> c11(A__PLUS(mark(x0), a__plus(a__U11(mark(z0), z1, z2), mark(x2))), MARK(plus(U11(z0, z1, z2), x2))) MARK(plus(x0, plus(U12(z0, z1, z2), x2))) -> c11(A__PLUS(mark(x0), a__plus(a__U12(mark(z0), z1, z2), mark(x2))), MARK(plus(U12(z0, z1, z2), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c11(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))) -> c11(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c11(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(x0, plus(0, x2))) -> c11(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(U11(z0, z1, z2), plus(x1, x2))) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(U12(z0, z1, z2), plus(x1, x2))) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c11(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c11(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c11(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c11(MARK(plus(x1, x2))) MARK(plus(U11(x0, x1, x2), s(z0))) -> c11(A__PLUS(a__U11(mark(x0), x1, x2), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(x0, z1, z2), x3)) -> c11(A__PLUS(U11(mark(x0), z1, z2), mark(x3)), MARK(x3)) MARK(plus(U11(U11(z0, z1, z2), x1, x2), x3)) -> c11(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(U12(z0, z1, z2), x1, x2), x3)) -> c11(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(plus(z0, z1), x1, x2), x3)) -> c11(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(tt, x1, x2), x3)) -> c11(A__PLUS(a__U11(tt, x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(s(z0), x1, x2), x3)) -> c11(A__PLUS(a__U11(s(mark(z0)), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(0, x1, x2), x3)) -> c11(A__PLUS(a__U11(0, x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(x0, x1, x2), 0)) -> c11(A__PLUS(a__U11(mark(x0), x1, x2), 0)) MARK(plus(U12(x0, x1, x2), s(z0))) -> c11(A__PLUS(a__U12(mark(x0), x1, x2), s(mark(z0))), MARK(s(z0))) MARK(plus(U12(x0, x1, x2), 0)) -> c11(A__PLUS(a__U12(mark(x0), x1, x2), 0), MARK(0)) MARK(plus(U12(x0, z1, z2), x3)) -> c11(A__PLUS(U12(mark(x0), z1, z2), mark(x3)), MARK(x3)) MARK(plus(U12(U11(z0, z1, z2), x1, x2), x3)) -> c11(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(U12(z0, z1, z2), x1, x2), x3)) -> c11(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(plus(z0, z1), x1, x2), x3)) -> c11(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(tt, x1, x2), x3)) -> c11(A__PLUS(a__U12(tt, x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(s(z0), x1, x2), x3)) -> c11(A__PLUS(a__U12(s(mark(z0)), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(0, x1, x2), x3)) -> c11(A__PLUS(a__U12(0, x1, x2), mark(x3)), MARK(x3)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_1, c9_1, c10_2, c10_1, c11_2, c11_1, c8_2, c9_2 ---------------------------------------- (223) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (224) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, 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mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U12(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c3(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c3(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U12(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U12(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U12(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, 0) -> c3(A__PLUS(0, 0)) MARK(U11(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U11(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U11(U11(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U11(U11(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U11(U11(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U11(U11(x0, z1, z2), x3, x4)) -> c8(MARK(U11(x0, z1, z2))) MARK(U11(U11(0, x1, x2), x3, x4)) -> c8(A__U11(a__U11(0, x1, x2), x3, x4)) MARK(U11(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U11(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U11(U12(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U11(U12(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U11(U12(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U11(U12(x0, z1, z2), x3, x4)) -> c8(MARK(U12(x0, z1, z2))) MARK(U11(U12(0, x1, x2), x3, x4)) -> c8(A__U11(a__U12(0, x1, x2), x3, x4)) MARK(U11(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U11(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U11(plus(x0, plus(z0, z1)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U11(plus(x0, tt), x2, x3)) -> c8(A__U11(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U11(plus(x0, s(z0)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U11(plus(x0, 0), x2, x3)) -> c8(A__U11(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U11(plus(U11(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U11(plus(U12(z0, z1, z2), x1), x2, x3)) -> c8(A__U11(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U11(plus(plus(z0, z1), x1), x2, x3)) -> c8(A__U11(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U11(plus(tt, x1), x2, x3)) -> c8(A__U11(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U11(plus(s(z0), x1), x2, x3)) -> c8(A__U11(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U11(plus(0, x1), x2, x3)) -> c8(A__U11(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U11(plus(x0, x1), x2, x3)) -> c8(MARK(plus(x0, x1))) MARK(U12(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U12(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U12(U11(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U12(U11(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U12(U11(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U12(U11(x0, z1, z2), x3, x4)) -> c9(MARK(U11(x0, z1, z2))) MARK(U12(U11(0, x1, x2), x3, x4)) -> c9(A__U12(a__U11(0, x1, x2), x3, x4)) MARK(U12(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U12(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U12(U12(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U12(U12(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U12(U12(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U12(U12(x0, z1, z2), x3, x4)) -> c9(MARK(U12(x0, z1, z2))) MARK(U12(U12(0, x1, x2), x3, x4)) -> c9(A__U12(a__U12(0, x1, x2), x3, x4)) MARK(U12(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U12(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U12(plus(x0, plus(z0, z1)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U12(plus(x0, tt), x2, x3)) -> c9(A__U12(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U12(plus(x0, s(z0)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U12(plus(x0, 0), x2, x3)) -> c9(A__U12(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U12(plus(U11(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U12(plus(U12(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U12(plus(plus(z0, z1), x1), x2, x3)) -> c9(A__U12(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U12(plus(tt, x1), x2, x3)) -> c9(A__U12(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U12(plus(s(z0), x1), x2, x3)) -> c9(A__U12(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U12(plus(0, x1), x2, x3)) -> c9(A__U12(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U12(plus(x0, x1), x2, x3)) -> c9(MARK(plus(x0, x1))) MARK(plus(x0, U11(U11(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__U11(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U11(U12(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__U12(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U11(plus(z0, z1), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(tt, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U11(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(0, x2, x3))) 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c11(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(tt, x1, x2), x3)) -> c11(A__PLUS(a__U11(tt, x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(s(z0), x1, x2), x3)) -> c11(A__PLUS(a__U11(s(mark(z0)), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(0, x1, x2), x3)) -> c11(A__PLUS(a__U11(0, x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(x0, x1, x2), 0)) -> c11(A__PLUS(a__U11(mark(x0), x1, x2), 0)) MARK(plus(U12(x0, x1, x2), s(z0))) -> c11(A__PLUS(a__U12(mark(x0), x1, x2), s(mark(z0))), MARK(s(z0))) MARK(plus(U12(x0, z1, z2), x3)) -> c11(A__PLUS(U12(mark(x0), z1, z2), mark(x3)), MARK(x3)) MARK(plus(U12(U11(z0, z1, z2), x1, x2), x3)) -> c11(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(U12(z0, z1, z2), x1, x2), x3)) -> c11(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(plus(z0, z1), x1, x2), x3)) -> c11(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(tt, x1, x2), x3)) -> c11(A__PLUS(a__U12(tt, x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(s(z0), x1, x2), x3)) -> c11(A__PLUS(a__U12(s(mark(z0)), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(0, x1, x2), x3)) -> c11(A__PLUS(a__U12(0, x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(x0, x1, x2), 0)) -> c11(A__PLUS(a__U12(mark(x0), x1, x2), 0)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), 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x1, x2), 0), MARK(U12(x0, x1, x2))) MARK(plus(U12(x0, z1, z2), x3)) -> c10(A__PLUS(U12(mark(x0), z1, z2), mark(x3)), MARK(U12(x0, z1, z2))) MARK(plus(U12(U11(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(plus(U12(U12(z0, z1, z2), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(plus(U12(plus(z0, z1), x1, x2), x3)) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(U12(plus(z0, z1), x1, x2))) MARK(plus(U12(tt, x1, x2), x3)) -> c10(A__PLUS(a__U12(tt, x1, x2), mark(x3)), MARK(U12(tt, x1, x2))) MARK(plus(U12(s(z0), x1, x2), x3)) -> c10(A__PLUS(a__U12(s(mark(z0)), x1, x2), mark(x3)), MARK(U12(s(z0), x1, x2))) MARK(plus(U12(x0, x1, x2), tt)) -> c10(MARK(U12(x0, x1, x2))) MARK(plus(U12(0, x1, x2), x3)) -> c10(A__PLUS(a__U12(0, x1, x2), mark(x3))) MARK(plus(plus(x0, x1), s(z0))) -> c10(A__PLUS(a__plus(mark(x0), mark(x1)), s(mark(z0))), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), 0)) -> c10(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c10(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, U11(z0, z1, z2)), x2)) -> c10(A__PLUS(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), mark(x2)), MARK(plus(x0, U11(z0, z1, z2)))) MARK(plus(plus(x0, U12(z0, z1, z2)), x2)) -> c10(A__PLUS(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), mark(x2)), MARK(plus(x0, U12(z0, z1, z2)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c10(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)) -> c10(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, s(z0)), x2)) -> c10(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(x0, 0), x2)) -> c10(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(U11(z0, z1, z2), x1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(plus(U11(z0, z1, z2), x1))) MARK(plus(plus(U12(z0, z1, z2), x1), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(plus(U12(z0, z1, z2), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c10(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)) -> c10(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(0, x1), x2)) -> c10(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(x0, x1), tt)) -> c10(MARK(plus(x0, x1))) MARK(plus(s(x0), s(z0))) -> c10(A__PLUS(s(mark(x0)), s(mark(z0))), MARK(s(x0))) MARK(plus(s(x0), 0)) -> c10(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(U11(z0, z1, z2)), x1)) -> c10(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x1)), MARK(s(U11(z0, z1, z2)))) MARK(plus(s(U12(z0, z1, z2)), x1)) -> c10(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x1)), MARK(s(U12(z0, z1, z2)))) MARK(plus(s(plus(z0, z1)), x1)) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c10(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(s(z0)), x1)) -> c10(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(0), x1)) -> c10(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(x0), x1)) -> c10(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c10(MARK(s(x0))) MARK(plus(tt, s(z0))) -> c10(A__PLUS(tt, s(mark(z0)))) MARK(plus(tt, 0)) -> c10(A__PLUS(tt, 0)) MARK(plus(0, s(z0))) -> c10(A__PLUS(0, s(mark(z0)))) MARK(plus(0, 0)) -> c10(A__PLUS(0, 0)) MARK(plus(x0, U11(U11(z0, z1, z2), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(a__U11(mark(z0), z1, z2), x2, x3)), MARK(U11(U11(z0, z1, z2), x2, x3))) MARK(plus(x0, U11(U12(z0, z1, z2), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(a__U12(mark(z0), z1, z2), x2, x3)), MARK(U11(U12(z0, z1, z2), x2, x3))) MARK(plus(x0, U11(plus(z0, z1), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(U11(plus(z0, z1), x2, x3))) MARK(plus(x0, U11(tt, x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(tt, x2, x3)), MARK(U11(tt, x2, x3))) MARK(plus(x0, U11(s(z0), x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(s(mark(z0)), x2, x3)), MARK(U11(s(z0), x2, x3))) MARK(plus(U11(z0, z1, z2), U11(x1, x2, x3))) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(U12(z0, z1, z2), U11(x1, x2, x3))) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(plus(z0, z1), U11(x1, x2, x3))) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(tt, U11(x1, x2, x3))) -> c11(A__PLUS(tt, a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(s(z0), U11(x1, x2, x3))) -> c11(A__PLUS(s(mark(z0)), a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(0, U11(x1, x2, x3))) -> c11(A__PLUS(0, a__U11(mark(x1), x2, x3)), MARK(U11(x1, x2, x3))) MARK(plus(x0, U11(x1, z1, z2))) -> c11(MARK(U11(x1, z1, z2))) MARK(plus(x0, U11(0, x2, x3))) -> c11(A__PLUS(mark(x0), a__U11(0, x2, x3))) MARK(plus(x0, U12(U11(z0, z1, z2), x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(a__U11(mark(z0), z1, z2), x2, x3)), MARK(U12(U11(z0, z1, z2), x2, x3))) MARK(plus(x0, U12(U12(z0, z1, z2), x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(a__U12(mark(z0), z1, z2), x2, x3)), MARK(U12(U12(z0, z1, z2), x2, x3))) MARK(plus(x0, U12(plus(z0, z1), x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(U12(plus(z0, z1), x2, x3))) MARK(plus(x0, U12(tt, x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(tt, x2, x3)), MARK(U12(tt, x2, x3))) MARK(plus(x0, U12(s(z0), x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(s(mark(z0)), x2, x3)), MARK(U12(s(z0), x2, x3))) MARK(plus(U11(z0, z1, z2), U12(x1, x2, x3))) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(U12(z0, z1, z2), U12(x1, x2, x3))) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(plus(z0, z1), U12(x1, x2, x3))) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(tt, U12(x1, x2, x3))) -> c11(A__PLUS(tt, a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(s(z0), U12(x1, x2, x3))) -> c11(A__PLUS(s(mark(z0)), a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(0, U12(x1, x2, x3))) -> c11(A__PLUS(0, a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(x0, U12(x1, z1, z2))) -> c11(MARK(U12(x1, z1, z2))) MARK(plus(x0, U12(0, x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(0, x2, x3))) MARK(plus(x0, plus(x1, U11(z0, z1, z2)))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), a__U11(mark(z0), z1, z2))), MARK(plus(x1, U11(z0, z1, z2)))) MARK(plus(x0, plus(x1, U12(z0, z1, z2)))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), a__U12(mark(z0), z1, z2))), MARK(plus(x1, U12(z0, z1, z2)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c11(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))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, s(z0)))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(x1, 0))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(U11(z0, z1, z2), x2))) -> c11(A__PLUS(mark(x0), a__plus(a__U11(mark(z0), z1, z2), mark(x2))), MARK(plus(U11(z0, z1, z2), x2))) MARK(plus(x0, plus(U12(z0, z1, z2), x2))) -> c11(A__PLUS(mark(x0), a__plus(a__U12(mark(z0), z1, z2), mark(x2))), MARK(plus(U12(z0, z1, z2), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c11(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))) -> c11(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c11(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(x0, plus(0, x2))) -> c11(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(U11(z0, z1, z2), plus(x1, x2))) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(U12(z0, z1, z2), plus(x1, x2))) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c11(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c11(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c11(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c11(MARK(plus(x1, x2))) MARK(plus(U11(x0, x1, x2), s(z0))) -> c11(A__PLUS(a__U11(mark(x0), x1, x2), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(x0, z1, z2), x3)) -> c11(A__PLUS(U11(mark(x0), z1, z2), mark(x3)), MARK(x3)) MARK(plus(U11(U11(z0, z1, z2), x1, x2), x3)) -> c11(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(U12(z0, z1, z2), x1, x2), x3)) -> c11(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(plus(z0, z1), x1, x2), x3)) -> c11(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(tt, x1, x2), x3)) -> c11(A__PLUS(a__U11(tt, x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(s(z0), x1, x2), x3)) -> c11(A__PLUS(a__U11(s(mark(z0)), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(0, x1, x2), x3)) -> c11(A__PLUS(a__U11(0, x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(x0, x1, x2), 0)) -> c11(A__PLUS(a__U11(mark(x0), x1, x2), 0)) MARK(plus(U12(x0, x1, x2), s(z0))) -> c11(A__PLUS(a__U12(mark(x0), x1, x2), s(mark(z0))), MARK(s(z0))) MARK(plus(U12(x0, z1, z2), x3)) -> c11(A__PLUS(U12(mark(x0), z1, z2), mark(x3)), MARK(x3)) MARK(plus(U12(U11(z0, z1, z2), x1, x2), x3)) -> c11(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(U12(z0, z1, z2), x1, x2), x3)) -> c11(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(plus(z0, z1), x1, x2), x3)) -> c11(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(tt, x1, x2), x3)) -> c11(A__PLUS(a__U12(tt, x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(s(z0), x1, x2), x3)) -> c11(A__PLUS(a__U12(s(mark(z0)), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(0, x1, x2), x3)) -> c11(A__PLUS(a__U12(0, x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(x0, x1, x2), 0)) -> c11(A__PLUS(a__U12(mark(x0), x1, x2), 0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_1, c9_1, c10_2, c10_1, c11_2, c11_1, c8_2, c9_2 ---------------------------------------- (225) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(plus(z0, z1), x1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) by MARK(plus(plus(x0, x1), U11(z0, z1, z2))) -> c11(A__PLUS(a__plus(mark(x0), mark(x1)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(plus(x0, x1), U12(z0, z1, z2))) -> c11(A__PLUS(a__plus(mark(x0), mark(x1)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(plus(x0, x1), plus(z0, z1))) -> c11(A__PLUS(a__plus(mark(x0), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(plus(x0, x1), tt)) -> c11(A__PLUS(a__plus(mark(x0), mark(x1)), tt), MARK(tt)) MARK(plus(plus(x0, x1), s(z0))) -> c11(A__PLUS(a__plus(mark(x0), mark(x1)), s(mark(z0))), MARK(s(z0))) MARK(plus(plus(x0, x1), 0)) -> c11(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(0)) MARK(plus(plus(x0, x1), x2)) -> c11(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, U11(z0, z1, z2)), x2)) -> c11(A__PLUS(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, U12(z0, z1, z2)), x2)) -> c11(A__PLUS(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c11(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, tt), x2)) -> c11(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) MARK(plus(plus(x0, s(z0)), x2)) -> c11(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, 0), x2)) -> c11(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) MARK(plus(plus(U11(z0, z1, z2), x1), x2)) -> c11(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(U12(z0, z1, z2), x1), x2)) -> c11(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c11(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c11(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c11(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c11(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) ---------------------------------------- (226) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U12(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c3(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c3(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U12(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U12(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U12(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, 0) -> c3(A__PLUS(0, 0)) MARK(U11(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U11(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U11(U11(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U11(U11(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U11(U11(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U11(U11(x0, z1, z2), x3, x4)) -> c8(MARK(U11(x0, z1, z2))) MARK(U11(U11(0, x1, x2), x3, x4)) -> c8(A__U11(a__U11(0, x1, x2), x3, x4)) MARK(U11(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U11(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U11(U12(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U11(U12(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U11(U12(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U11(U12(x0, z1, z2), x3, x4)) -> c8(MARK(U12(x0, z1, z2))) MARK(U11(U12(0, x1, x2), x3, x4)) -> c8(A__U11(a__U12(0, x1, x2), x3, x4)) MARK(U11(plus(x0, U11(z0, z1, z2)), x2, x3)) -> 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z1), x1), x2, x3)) -> c8(A__U11(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U11(plus(tt, x1), x2, x3)) -> c8(A__U11(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U11(plus(s(z0), x1), x2, x3)) -> c8(A__U11(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U11(plus(0, x1), x2, x3)) -> c8(A__U11(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U11(plus(x0, x1), x2, x3)) -> c8(MARK(plus(x0, x1))) MARK(U12(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U12(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U12(U11(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U12(U11(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U12(U11(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U12(U11(x0, z1, z2), x3, x4)) -> c9(MARK(U11(x0, z1, z2))) MARK(U12(U11(0, x1, x2), x3, x4)) -> c9(A__U12(a__U11(0, x1, x2), x3, x4)) MARK(U12(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U12(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U12(U12(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U12(U12(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U12(U12(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U12(U12(x0, z1, z2), x3, x4)) -> c9(MARK(U12(x0, z1, z2))) MARK(U12(U12(0, x1, x2), x3, x4)) -> c9(A__U12(a__U12(0, x1, x2), x3, x4)) MARK(U12(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U12(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U12(plus(x0, plus(z0, z1)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U12(plus(x0, tt), x2, x3)) -> c9(A__U12(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U12(plus(x0, s(z0)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U12(plus(x0, 0), x2, x3)) -> c9(A__U12(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U12(plus(U11(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U12(plus(U12(z0, z1, z2), x1), x2, x3)) 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x3))) -> c10(A__PLUS(mark(x0), a__U11(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U11(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U11(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(s(z0), U11(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(x0, U11(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U11(x1, x2, x3))) -> c10(A__PLUS(tt, a__U11(mark(x1), x2, x3))) MARK(plus(0, U11(x1, x2, x3))) -> c10(A__PLUS(0, a__U11(mark(x1), x2, x3))) MARK(plus(x0, U12(U11(z0, z1, z2), x2, 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x2)) -> c11(A__PLUS(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, U12(z0, z1, z2)), x2)) -> c11(A__PLUS(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c11(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, tt), x2)) -> c11(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) MARK(plus(plus(x0, s(z0)), x2)) -> c11(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, 0), x2)) -> c11(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) MARK(plus(plus(U11(z0, z1, z2), x1), x2)) -> c11(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(U12(z0, z1, z2), x1), x2)) -> c11(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c11(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c11(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c11(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c11(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), 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c11(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(x0, plus(0, x2))) -> c11(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(U11(z0, z1, z2), plus(x1, x2))) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(U12(z0, z1, z2), plus(x1, x2))) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c11(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c11(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c11(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c11(MARK(plus(x1, x2))) MARK(plus(U11(x0, x1, x2), s(z0))) -> c11(A__PLUS(a__U11(mark(x0), x1, x2), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(x0, z1, z2), x3)) -> c11(A__PLUS(U11(mark(x0), z1, z2), mark(x3)), MARK(x3)) MARK(plus(U11(U11(z0, z1, z2), x1, x2), x3)) -> c11(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(U12(z0, z1, z2), x1, x2), x3)) -> c11(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(plus(z0, z1), x1, x2), x3)) -> c11(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(tt, x1, x2), x3)) -> c11(A__PLUS(a__U11(tt, x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(s(z0), x1, x2), x3)) -> c11(A__PLUS(a__U11(s(mark(z0)), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(0, x1, x2), x3)) -> c11(A__PLUS(a__U11(0, x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(x0, x1, x2), 0)) -> c11(A__PLUS(a__U11(mark(x0), x1, x2), 0)) MARK(plus(U12(x0, x1, x2), s(z0))) -> c11(A__PLUS(a__U12(mark(x0), x1, x2), s(mark(z0))), MARK(s(z0))) MARK(plus(U12(x0, z1, z2), x3)) -> c11(A__PLUS(U12(mark(x0), z1, z2), mark(x3)), MARK(x3)) MARK(plus(U12(U11(z0, z1, z2), x1, x2), x3)) -> c11(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(U12(z0, z1, z2), x1, x2), x3)) -> c11(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(plus(z0, z1), x1, x2), x3)) -> c11(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(tt, x1, x2), x3)) -> c11(A__PLUS(a__U12(tt, x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(s(z0), x1, x2), x3)) -> c11(A__PLUS(a__U12(s(mark(z0)), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(0, x1, x2), x3)) -> c11(A__PLUS(a__U12(0, x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(x0, x1, x2), 0)) -> c11(A__PLUS(a__U12(mark(x0), x1, x2), 0)) MARK(plus(plus(x0, x1), tt)) -> c11(A__PLUS(a__plus(mark(x0), mark(x1)), tt), MARK(tt)) MARK(plus(plus(x0, x1), s(z0))) -> c11(A__PLUS(a__plus(mark(x0), mark(x1)), s(mark(z0))), MARK(s(z0))) MARK(plus(plus(x0, x1), 0)) -> c11(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(0)) MARK(plus(plus(x0, x1), x2)) -> c11(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, U11(z0, z1, z2)), x2)) -> c11(A__PLUS(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, U12(z0, z1, z2)), x2)) -> c11(A__PLUS(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c11(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, tt), x2)) -> c11(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) MARK(plus(plus(x0, s(z0)), x2)) -> c11(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, 0), x2)) -> c11(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) MARK(plus(plus(U11(z0, z1, z2), x1), x2)) -> c11(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(U12(z0, z1, z2), x1), x2)) -> c11(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c11(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c11(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c11(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c11(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_1, c9_1, c10_2, c10_1, c11_2, c11_1, c8_2, c9_2 ---------------------------------------- (227) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(plus(plus(x0, x1), tt)) -> c11(A__PLUS(a__plus(mark(x0), mark(x1)), tt), MARK(tt)) ---------------------------------------- (228) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, 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c11(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c11(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c11(MARK(plus(x1, x2))) MARK(plus(U11(x0, x1, x2), s(z0))) -> c11(A__PLUS(a__U11(mark(x0), x1, x2), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(x0, z1, z2), x3)) -> c11(A__PLUS(U11(mark(x0), z1, z2), mark(x3)), MARK(x3)) MARK(plus(U11(U11(z0, z1, z2), x1, x2), x3)) -> c11(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(U12(z0, z1, z2), x1, x2), x3)) -> c11(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(plus(z0, z1), x1, x2), x3)) -> c11(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(tt, x1, x2), x3)) -> c11(A__PLUS(a__U11(tt, x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(s(z0), x1, x2), x3)) -> c11(A__PLUS(a__U11(s(mark(z0)), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(0, x1, 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x2), 0)) -> c11(A__PLUS(a__U12(mark(x0), x1, x2), 0)) MARK(plus(plus(x0, x1), s(z0))) -> c11(A__PLUS(a__plus(mark(x0), mark(x1)), s(mark(z0))), MARK(s(z0))) MARK(plus(plus(x0, x1), 0)) -> c11(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(0)) MARK(plus(plus(x0, x1), x2)) -> c11(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, U11(z0, z1, z2)), x2)) -> c11(A__PLUS(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, U12(z0, z1, z2)), x2)) -> c11(A__PLUS(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c11(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, tt), x2)) -> c11(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) MARK(plus(plus(x0, s(z0)), x2)) -> c11(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, 0), x2)) -> c11(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) MARK(plus(plus(U11(z0, z1, z2), x1), x2)) -> c11(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(U12(z0, z1, z2), x1), x2)) -> c11(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c11(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c11(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c11(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c11(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> 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MARK(plus(U11(0, x1, x2), x3)) -> c11(A__PLUS(a__U11(0, x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(x0, x1, x2), 0)) -> c11(A__PLUS(a__U11(mark(x0), x1, x2), 0)) MARK(plus(U12(x0, x1, x2), s(z0))) -> c11(A__PLUS(a__U12(mark(x0), x1, x2), s(mark(z0))), MARK(s(z0))) MARK(plus(U12(x0, z1, z2), x3)) -> c11(A__PLUS(U12(mark(x0), z1, z2), mark(x3)), MARK(x3)) MARK(plus(U12(U11(z0, z1, z2), x1, x2), x3)) -> c11(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(U12(z0, z1, z2), x1, x2), x3)) -> c11(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(plus(z0, z1), x1, x2), x3)) -> c11(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(tt, x1, x2), x3)) -> c11(A__PLUS(a__U12(tt, x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(s(z0), x1, x2), x3)) -> c11(A__PLUS(a__U12(s(mark(z0)), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(0, x1, x2), x3)) -> c11(A__PLUS(a__U12(0, x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(x0, x1, x2), 0)) -> c11(A__PLUS(a__U12(mark(x0), x1, x2), 0)) MARK(plus(plus(x0, x1), s(z0))) -> c11(A__PLUS(a__plus(mark(x0), mark(x1)), s(mark(z0))), MARK(s(z0))) MARK(plus(plus(x0, x1), 0)) -> c11(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(0)) MARK(plus(plus(x0, x1), x2)) -> c11(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, U11(z0, z1, z2)), x2)) -> c11(A__PLUS(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, U12(z0, z1, z2)), x2)) -> c11(A__PLUS(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c11(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, tt), x2)) -> c11(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) MARK(plus(plus(x0, s(z0)), x2)) -> c11(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, 0), x2)) -> c11(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) MARK(plus(plus(U11(z0, z1, z2), x1), x2)) -> c11(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(U12(z0, z1, z2), x1), x2)) -> c11(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c11(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c11(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c11(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c11(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_1, c9_1, c10_2, c10_1, c11_2, c11_1, c8_2, c9_2 ---------------------------------------- (229) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (230) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> 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z2), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(U12(z0, z1, z2), x1), x2)) -> c11(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c11(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c11(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c11(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c11(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, x1), 0)) -> c11(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> 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MARK(plus(U11(0, x1, x2), x3)) -> c11(A__PLUS(a__U11(0, x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(x0, x1, x2), 0)) -> c11(A__PLUS(a__U11(mark(x0), x1, x2), 0)) MARK(plus(U12(x0, x1, x2), s(z0))) -> c11(A__PLUS(a__U12(mark(x0), x1, x2), s(mark(z0))), MARK(s(z0))) MARK(plus(U12(x0, z1, z2), x3)) -> c11(A__PLUS(U12(mark(x0), z1, z2), mark(x3)), MARK(x3)) MARK(plus(U12(U11(z0, z1, z2), x1, x2), x3)) -> c11(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(U12(z0, z1, z2), x1, x2), x3)) -> c11(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(plus(z0, z1), x1, x2), x3)) -> c11(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(tt, x1, x2), x3)) -> c11(A__PLUS(a__U12(tt, x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(s(z0), x1, x2), x3)) -> c11(A__PLUS(a__U12(s(mark(z0)), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(0, x1, x2), x3)) -> c11(A__PLUS(a__U12(0, x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(x0, x1, x2), 0)) -> c11(A__PLUS(a__U12(mark(x0), x1, x2), 0)) MARK(plus(plus(x0, x1), s(z0))) -> c11(A__PLUS(a__plus(mark(x0), mark(x1)), s(mark(z0))), MARK(s(z0))) MARK(plus(plus(x0, x1), x2)) -> c11(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, U11(z0, z1, z2)), x2)) -> c11(A__PLUS(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, U12(z0, z1, z2)), x2)) -> c11(A__PLUS(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c11(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, tt), x2)) -> c11(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) MARK(plus(plus(x0, s(z0)), x2)) -> c11(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, 0), x2)) -> c11(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) MARK(plus(plus(U11(z0, z1, z2), x1), x2)) -> c11(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(U12(z0, z1, z2), x1), x2)) -> c11(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c11(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c11(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c11(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c11(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, x1), 0)) -> c11(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_1, c9_1, c10_2, c10_1, c11_2, c11_1, c8_2, c9_2 ---------------------------------------- (231) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(tt, x1)) -> c11(A__PLUS(tt, mark(x1)), MARK(x1)) by MARK(plus(tt, U11(z0, z1, z2))) -> c11(A__PLUS(tt, a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(tt, U12(z0, z1, z2))) -> c11(A__PLUS(tt, a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(tt, plus(z0, z1))) -> c11(A__PLUS(tt, a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(tt, tt)) -> c11(A__PLUS(tt, tt), MARK(tt)) MARK(plus(tt, s(z0))) -> c11(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) MARK(plus(tt, 0)) -> c11(A__PLUS(tt, 0), MARK(0)) ---------------------------------------- (232) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U12(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c3(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c3(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U12(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U12(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U12(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, 0) -> c3(A__PLUS(0, 0)) MARK(U11(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U11(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U11(U11(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U11(U11(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U11(U11(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U11(U11(x0, z1, z2), x3, x4)) -> c8(MARK(U11(x0, z1, z2))) MARK(U11(U11(0, x1, x2), x3, x4)) -> c8(A__U11(a__U11(0, x1, x2), x3, x4)) MARK(U11(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U11(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U11(U12(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U11(U12(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U11(U12(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U11(U12(x0, z1, z2), x3, x4)) -> c8(MARK(U12(x0, z1, z2))) MARK(U11(U12(0, x1, x2), x3, x4)) -> c8(A__U11(a__U12(0, x1, x2), x3, x4)) MARK(U11(plus(x0, U11(z0, z1, z2)), x2, x3)) -> 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z1), x1), x2, x3)) -> c8(A__U11(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U11(plus(tt, x1), x2, x3)) -> c8(A__U11(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U11(plus(s(z0), x1), x2, x3)) -> c8(A__U11(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U11(plus(0, x1), x2, x3)) -> c8(A__U11(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U11(plus(x0, x1), x2, x3)) -> c8(MARK(plus(x0, x1))) MARK(U12(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U12(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U12(U11(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U12(U11(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U12(U11(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U12(U11(x0, z1, z2), x3, x4)) -> c9(MARK(U11(x0, z1, z2))) MARK(U12(U11(0, x1, x2), x3, x4)) -> c9(A__U12(a__U11(0, x1, x2), x3, x4)) MARK(U12(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U12(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U12(U12(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U12(U12(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U12(U12(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U12(U12(x0, z1, z2), x3, x4)) -> c9(MARK(U12(x0, z1, z2))) MARK(U12(U12(0, x1, x2), x3, x4)) -> c9(A__U12(a__U12(0, x1, x2), x3, x4)) MARK(U12(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U12(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U12(plus(x0, plus(z0, z1)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U12(plus(x0, tt), x2, x3)) -> c9(A__U12(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U12(plus(x0, s(z0)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U12(plus(x0, 0), x2, x3)) -> c9(A__U12(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U12(plus(U11(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U12(plus(U12(z0, z1, z2), x1), x2, x3)) 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x3))) -> c10(A__PLUS(mark(x0), a__U11(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U11(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U11(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(s(z0), U11(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(x0, U11(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U11(x1, x2, x3))) -> c10(A__PLUS(tt, a__U11(mark(x1), x2, x3))) MARK(plus(0, U11(x1, x2, x3))) -> c10(A__PLUS(0, a__U11(mark(x1), x2, x3))) MARK(plus(x0, U12(U11(z0, z1, z2), x2, 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a__U12(mark(z0), z1, z2)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c11(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, tt), x2)) -> c11(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) MARK(plus(plus(x0, s(z0)), x2)) -> c11(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, 0), x2)) -> c11(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) MARK(plus(plus(U11(z0, z1, z2), x1), x2)) -> c11(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(U12(z0, z1, z2), x1), x2)) -> c11(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c11(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c11(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c11(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c11(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, x1), 0)) -> c11(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) MARK(plus(tt, tt)) -> c11(A__PLUS(tt, tt), MARK(tt)) MARK(plus(tt, s(z0))) -> c11(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) MARK(plus(tt, 0)) -> c11(A__PLUS(tt, 0), MARK(0)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), 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MARK(x2)) MARK(plus(plus(x0, U11(z0, z1, z2)), x2)) -> c11(A__PLUS(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, U12(z0, z1, z2)), x2)) -> c11(A__PLUS(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c11(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, tt), x2)) -> c11(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) MARK(plus(plus(x0, s(z0)), x2)) -> c11(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, 0), x2)) -> c11(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) MARK(plus(plus(U11(z0, z1, z2), x1), x2)) -> c11(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(U12(z0, z1, z2), x1), x2)) -> c11(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c11(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c11(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c11(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c11(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, x1), 0)) -> c11(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) MARK(plus(tt, tt)) -> c11(A__PLUS(tt, tt), MARK(tt)) MARK(plus(tt, s(z0))) -> c11(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) MARK(plus(tt, 0)) -> c11(A__PLUS(tt, 0), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_1, c9_1, c10_2, c10_1, c11_2, c11_1, c8_2, c9_2 ---------------------------------------- (233) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(plus(tt, tt)) -> c11(A__PLUS(tt, tt), MARK(tt)) ---------------------------------------- (234) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, 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mark(x2)), MARK(x2)) MARK(plus(plus(U12(z0, z1, z2), x1), x2)) -> c11(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c11(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c11(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c11(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c11(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, x1), 0)) -> c11(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) MARK(plus(tt, s(z0))) -> c11(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) MARK(plus(tt, 0)) -> c11(A__PLUS(tt, 0), MARK(0)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, 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MARK(x3)) MARK(plus(U11(s(z0), x1, x2), x3)) -> c11(A__PLUS(a__U11(s(mark(z0)), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(0, x1, x2), x3)) -> c11(A__PLUS(a__U11(0, x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(x0, x1, x2), 0)) -> c11(A__PLUS(a__U11(mark(x0), x1, x2), 0)) MARK(plus(U12(x0, x1, x2), s(z0))) -> c11(A__PLUS(a__U12(mark(x0), x1, x2), s(mark(z0))), MARK(s(z0))) MARK(plus(U12(x0, z1, z2), x3)) -> c11(A__PLUS(U12(mark(x0), z1, z2), mark(x3)), MARK(x3)) MARK(plus(U12(U11(z0, z1, z2), x1, x2), x3)) -> c11(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(U12(z0, z1, z2), x1, x2), x3)) -> c11(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(plus(z0, z1), x1, x2), x3)) -> c11(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(tt, x1, x2), x3)) -> c11(A__PLUS(a__U12(tt, x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(s(z0), x1, x2), x3)) -> c11(A__PLUS(a__U12(s(mark(z0)), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(0, x1, x2), x3)) -> c11(A__PLUS(a__U12(0, x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(x0, x1, x2), 0)) -> c11(A__PLUS(a__U12(mark(x0), x1, x2), 0)) MARK(plus(plus(x0, x1), s(z0))) -> c11(A__PLUS(a__plus(mark(x0), mark(x1)), s(mark(z0))), MARK(s(z0))) MARK(plus(plus(x0, x1), x2)) -> c11(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, U11(z0, z1, z2)), x2)) -> c11(A__PLUS(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, U12(z0, z1, z2)), x2)) -> c11(A__PLUS(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c11(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, tt), x2)) -> c11(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) MARK(plus(plus(x0, s(z0)), x2)) -> c11(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, 0), x2)) -> c11(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) MARK(plus(plus(U11(z0, z1, z2), x1), x2)) -> c11(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(U12(z0, z1, z2), x1), x2)) -> c11(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c11(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c11(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c11(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c11(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, x1), 0)) -> c11(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) MARK(plus(tt, s(z0))) -> c11(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) MARK(plus(tt, 0)) -> c11(A__PLUS(tt, 0), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_1, c9_1, c10_2, c10_1, c11_2, c11_1, c8_2, c9_2 ---------------------------------------- (235) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (236) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U12(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U12(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c3(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c3(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U12(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U12(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U12(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, 0) -> c3(A__PLUS(0, 0)) MARK(U11(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U11(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U11(U11(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U11(U11(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U11(U11(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U11(U11(x0, z1, z2), x3, x4)) -> c8(MARK(U11(x0, z1, z2))) MARK(U11(U11(0, x1, x2), x3, x4)) -> c8(A__U11(a__U11(0, x1, x2), x3, x4)) MARK(U11(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U11(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U11(U12(plus(z0, z1), x1, x2), x3, x4)) -> c8(A__U11(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U11(U12(tt, x1, x2), x3, x4)) -> c8(A__U11(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U11(U12(s(z0), x1, x2), x3, x4)) -> c8(A__U11(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U11(U12(x0, z1, z2), x3, x4)) -> c8(MARK(U12(x0, z1, z2))) MARK(U11(U12(0, x1, x2), x3, x4)) -> c8(A__U11(a__U12(0, x1, x2), x3, x4)) MARK(U11(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U11(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U11(plus(x0, plus(z0, z1)), x2, x3)) -> c8(A__U11(a__plus(mark(x0), a__plus(mark(z0), 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MARK(U11(plus(0, x1), x2, x3)) -> c8(A__U11(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U11(plus(x0, x1), x2, x3)) -> c8(MARK(plus(x0, x1))) MARK(U12(U11(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U11(z0, z1, z2), x1, x2))) MARK(U12(U11(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U11(U12(z0, z1, z2), x1, x2))) MARK(U12(U11(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U11(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U11(plus(z0, z1), x1, x2))) MARK(U12(U11(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U11(tt, x1, x2), x3, x4), MARK(U11(tt, x1, x2))) MARK(U12(U11(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U11(s(mark(z0)), x1, x2), x3, x4), MARK(U11(s(z0), x1, x2))) MARK(U12(U11(x0, z1, z2), x3, x4)) -> c9(MARK(U11(x0, z1, z2))) MARK(U12(U11(0, x1, x2), x3, x4)) -> c9(A__U12(a__U11(0, x1, x2), x3, x4)) MARK(U12(U12(U11(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U11(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U11(z0, z1, z2), x1, x2))) MARK(U12(U12(U12(z0, z1, z2), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__U12(mark(z0), z1, z2), x1, x2), x3, x4), MARK(U12(U12(z0, z1, z2), x1, x2))) MARK(U12(U12(plus(z0, z1), x1, x2), x3, x4)) -> c9(A__U12(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), x3, x4), MARK(U12(plus(z0, z1), x1, x2))) MARK(U12(U12(tt, x1, x2), x3, x4)) -> c9(A__U12(a__U12(tt, x1, x2), x3, x4), MARK(U12(tt, x1, x2))) MARK(U12(U12(s(z0), x1, x2), x3, x4)) -> c9(A__U12(a__U12(s(mark(z0)), x1, x2), x3, x4), MARK(U12(s(z0), x1, x2))) MARK(U12(U12(x0, z1, z2), x3, x4)) -> c9(MARK(U12(x0, z1, z2))) MARK(U12(U12(0, x1, x2), x3, x4)) -> c9(A__U12(a__U12(0, x1, x2), x3, x4)) MARK(U12(plus(x0, U11(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U11(z0, z1, z2)))) MARK(U12(plus(x0, U12(z0, z1, z2)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), x2, x3), MARK(plus(x0, U12(z0, z1, z2)))) MARK(U12(plus(x0, plus(z0, z1)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2, x3), MARK(plus(x0, plus(z0, z1)))) MARK(U12(plus(x0, tt), x2, x3)) -> c9(A__U12(a__plus(mark(x0), tt), x2, x3), MARK(plus(x0, tt))) MARK(U12(plus(x0, s(z0)), x2, x3)) -> c9(A__U12(a__plus(mark(x0), s(mark(z0))), x2, x3), MARK(plus(x0, s(z0)))) MARK(U12(plus(x0, 0), x2, x3)) -> c9(A__U12(a__plus(mark(x0), 0), x2, x3), MARK(plus(x0, 0))) MARK(U12(plus(U11(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U11(z0, z1, z2), x1))) MARK(U12(plus(U12(z0, z1, z2), x1), x2, x3)) -> c9(A__U12(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), x2, x3), MARK(plus(U12(z0, z1, z2), x1))) MARK(U12(plus(plus(z0, z1), x1), x2, x3)) -> c9(A__U12(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2, x3), MARK(plus(plus(z0, z1), x1))) MARK(U12(plus(tt, x1), x2, x3)) -> c9(A__U12(a__plus(tt, mark(x1)), x2, x3), MARK(plus(tt, x1))) MARK(U12(plus(s(z0), x1), x2, x3)) -> c9(A__U12(a__plus(s(mark(z0)), mark(x1)), x2, x3), MARK(plus(s(z0), x1))) MARK(U12(plus(0, x1), x2, x3)) -> c9(A__U12(a__plus(0, mark(x1)), x2, x3), MARK(plus(0, x1))) MARK(U12(plus(x0, x1), x2, x3)) -> c9(MARK(plus(x0, x1))) MARK(plus(x0, U11(U11(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__U11(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U11(U12(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__U12(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U11(plus(z0, z1), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(tt, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U11(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U11(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U11(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U11(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U11(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(s(z0), U11(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(x0, U11(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U11(x1, x2, x3))) -> c10(A__PLUS(tt, a__U11(mark(x1), x2, x3))) MARK(plus(0, U11(x1, x2, x3))) -> c10(A__PLUS(0, a__U11(mark(x1), x2, x3))) MARK(plus(x0, U12(U11(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__U11(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U12(U12(z0, z1, z2), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__U12(mark(z0), z1, z2), x2, x3)), MARK(x0)) MARK(plus(x0, U12(plus(z0, z1), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(a__plus(mark(z0), mark(z1)), x2, x3)), MARK(x0)) MARK(plus(x0, U12(tt, x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(tt, x2, x3)), MARK(x0)) MARK(plus(x0, U12(s(z0), x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(s(mark(z0)), x2, x3)), MARK(x0)) MARK(plus(x0, U12(0, x2, x3))) -> c10(A__PLUS(mark(x0), a__U12(0, x2, x3)), MARK(x0)) MARK(plus(U11(z0, z1, z2), U12(x1, x2, x3))) -> c10(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), U12(x1, x2, x3))) -> c10(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x1), x2, x3)), MARK(U12(z0, z1, z2))) MARK(plus(plus(z0, z1), U12(x1, x2, x3))) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x1), x2, x3)), MARK(plus(z0, z1))) MARK(plus(s(z0), U12(x1, x2, x3))) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x1), x2, x3)), MARK(s(z0))) MARK(plus(x0, U12(x1, z1, z2))) -> c10(MARK(x0)) MARK(plus(tt, U12(x1, x2, x3))) -> c10(A__PLUS(tt, a__U12(mark(x1), x2, x3))) MARK(plus(0, U12(x1, x2, x3))) -> c10(A__PLUS(0, a__U12(mark(x1), x2, x3))) MARK(plus(x0, 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0), mark(x2)), MARK(x2)) MARK(plus(plus(U11(z0, z1, z2), x1), x2)) -> c11(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(U12(z0, z1, z2), x1), x2)) -> c11(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c11(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c11(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c11(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c11(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, x1), 0)) -> c11(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) MARK(plus(tt, s(z0))) -> c11(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) MARK(plus(tt, 0)) -> c11(A__PLUS(tt, 0)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) A__PLUS(z0, 0) -> c5(MARK(z0)) A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) MARK(s(z0)) -> c13(MARK(z0)) A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U12(tt, tt, x1) -> c2(MARK(x1)) A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) MARK(U11(tt, x1, x2)) -> c8(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c8(MARK(s(z0))) MARK(U12(tt, x1, x2)) -> c9(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c9(MARK(s(z0))) MARK(plus(x0, s(z0))) -> c10(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c10(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c10(MARK(x0)) MARK(plus(x0, s(z0))) -> c11(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(s(z0), x1)) -> c11(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c11(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c11(A__PLUS(mark(x0), 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3)) A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3)) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3)) A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3)) A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3)) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0))) A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3)) A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2)) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3))) A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2))) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3))) A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3))) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3))) A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3))) A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0))) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3))) A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2))) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3))) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3))) A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3))) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3))) A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3))) A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0))) A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2)))) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2)))) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2))) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2)))) A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2)))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2))) A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2))) A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2))) A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2))) A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2))) A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2))) A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2))) A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2))) A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2))) A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2))) A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2))) A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2))) A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2))) A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2))) A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2))) A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2))) A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2)))) A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2)))) A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1))) A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1))) A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0)) A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0)) A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U12(tt, x0, plus(s(z0), x2)) -> 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c11(A__PLUS(0, a__U12(mark(x1), x2, x3)), MARK(U12(x1, x2, x3))) MARK(plus(x0, U12(x1, z1, z2))) -> c11(MARK(U12(x1, z1, z2))) MARK(plus(x0, U12(0, x2, x3))) -> c11(A__PLUS(mark(x0), a__U12(0, x2, x3))) MARK(plus(x0, plus(x1, U11(z0, z1, z2)))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), a__U11(mark(z0), z1, z2))), MARK(plus(x1, U11(z0, z1, z2)))) MARK(plus(x0, plus(x1, U12(z0, z1, z2)))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), a__U12(mark(z0), z1, z2))), MARK(plus(x1, U12(z0, z1, z2)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c11(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))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, s(z0)))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(x1, 0))) -> c11(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(U11(z0, z1, z2), x2))) -> c11(A__PLUS(mark(x0), a__plus(a__U11(mark(z0), z1, z2), mark(x2))), MARK(plus(U11(z0, z1, z2), x2))) MARK(plus(x0, plus(U12(z0, z1, z2), x2))) -> c11(A__PLUS(mark(x0), a__plus(a__U12(mark(z0), z1, z2), mark(x2))), MARK(plus(U12(z0, z1, z2), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c11(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))) -> c11(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c11(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(x0, plus(0, x2))) -> c11(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(U11(z0, z1, z2), plus(x1, x2))) -> c11(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(U12(z0, z1, z2), plus(x1, x2))) -> c11(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) 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mark(x3)), MARK(x3)) MARK(plus(U11(tt, x1, x2), x3)) -> c11(A__PLUS(a__U11(tt, x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(s(z0), x1, x2), x3)) -> c11(A__PLUS(a__U11(s(mark(z0)), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(0, x1, x2), x3)) -> c11(A__PLUS(a__U11(0, x1, x2), mark(x3)), MARK(x3)) MARK(plus(U11(x0, x1, x2), 0)) -> c11(A__PLUS(a__U11(mark(x0), x1, x2), 0)) MARK(plus(U12(x0, x1, x2), s(z0))) -> c11(A__PLUS(a__U12(mark(x0), x1, x2), s(mark(z0))), MARK(s(z0))) MARK(plus(U12(x0, z1, z2), x3)) -> c11(A__PLUS(U12(mark(x0), z1, z2), mark(x3)), MARK(x3)) MARK(plus(U12(U11(z0, z1, z2), x1, x2), x3)) -> c11(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(U12(z0, z1, z2), x1, x2), x3)) -> c11(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(plus(z0, z1), x1, x2), x3)) -> c11(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(tt, x1, x2), x3)) -> c11(A__PLUS(a__U12(tt, x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(s(z0), x1, x2), x3)) -> c11(A__PLUS(a__U12(s(mark(z0)), x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(0, x1, x2), x3)) -> c11(A__PLUS(a__U12(0, x1, x2), mark(x3)), MARK(x3)) MARK(plus(U12(x0, x1, x2), 0)) -> c11(A__PLUS(a__U12(mark(x0), x1, x2), 0)) MARK(plus(plus(x0, x1), s(z0))) -> c11(A__PLUS(a__plus(mark(x0), mark(x1)), s(mark(z0))), MARK(s(z0))) MARK(plus(plus(x0, x1), x2)) -> c11(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, U11(z0, z1, z2)), x2)) -> c11(A__PLUS(a__plus(mark(x0), a__U11(mark(z0), z1, z2)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, U12(z0, z1, z2)), x2)) -> c11(A__PLUS(a__plus(mark(x0), a__U12(mark(z0), z1, z2)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c11(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, tt), x2)) -> c11(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) MARK(plus(plus(x0, s(z0)), x2)) -> c11(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, 0), x2)) -> c11(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) MARK(plus(plus(U11(z0, z1, z2), x1), x2)) -> c11(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(U12(z0, z1, z2), x1), x2)) -> c11(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c11(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c11(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c11(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c11(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, x1), 0)) -> c11(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) MARK(plus(tt, s(z0))) -> c11(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) MARK(plus(tt, 0)) -> c11(A__PLUS(tt, 0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__PLUS_2, MARK_1, A__U12_3 Compound Symbols: c_1, c5_1, c6_1, c13_1, c2_2, c2_1, c3_2, c3_1, c8_1, c9_1, c10_2, c10_1, c11_2, c11_1, c8_2, c9_2