KILLED proof of input_loBSQnUIKl.trs # AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). (0) CpxTRS (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxTRS (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (4) CpxTRS (5) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (6) CdtProblem (7) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxRelTRS (9) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (10) CpxRelTRS (11) TypeInferenceProof [BOTH BOUNDS(ID, ID), 10 ms] (12) typed CpxTrs (13) OrderProof [LOWER BOUND(ID), 0 ms] (14) typed CpxTrs (15) RewriteLemmaProof [LOWER BOUND(ID), 856 ms] (16) typed CpxTrs (17) RewriteLemmaProof [LOWER BOUND(ID), 124 ms] (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 204 ms] (20) typed CpxTrs (21) RewriteLemmaProof [LOWER BOUND(ID), 169 ms] (22) typed CpxTrs (23) RewriteLemmaProof [LOWER BOUND(ID), 35 ms] (24) typed CpxTrs (25) RewriteLemmaProof [LOWER BOUND(ID), 187 ms] (26) typed CpxTrs (27) RewriteLemmaProof [LOWER BOUND(ID), 132 ms] (28) typed CpxTrs (29) RewriteLemmaProof [LOWER BOUND(ID), 333 ms] (30) BEST (31) proven lower bound (32) LowerBoundPropagationProof [FINISHED, 0 ms] (33) BOUNDS(n^1, INF) (34) typed CpxTrs (35) RewriteLemmaProof [LOWER BOUND(ID), 325 ms] (36) typed CpxTrs (37) RewriteLemmaProof [LOWER BOUND(ID), 1935 ms] (38) typed CpxTrs (39) RewriteLemmaProof [LOWER BOUND(ID), 347 ms] (40) typed CpxTrs (41) RewriteLemmaProof [LOWER BOUND(ID), 312 ms] (42) typed CpxTrs (43) RewriteLemmaProof [LOWER BOUND(ID), 289 ms] (44) typed CpxTrs (45) RewriteLemmaProof [LOWER BOUND(ID), 1634 ms] (46) BOUNDS(1, INF) (47) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (48) CdtProblem (49) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (50) CdtProblem (51) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (52) CpxRelTRS (53) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (54) CpxTRS (55) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (56) CpxWeightedTrs (57) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (58) CpxTypedWeightedTrs (59) CompletionProof [UPPER BOUND(ID), 0 ms] (60) CpxTypedWeightedCompleteTrs (61) NarrowingProof [BOTH BOUNDS(ID, ID), 104 ms] (62) CpxTypedWeightedCompleteTrs (63) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (64) CpxRNTS (65) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (66) CpxRNTS (67) CompletionProof [UPPER BOUND(ID), 0 ms] (68) CpxTypedWeightedCompleteTrs (69) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (70) CpxRNTS (71) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (72) CdtProblem (73) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (74) CdtProblem (75) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (76) CdtProblem (77) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (78) CdtProblem (79) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (80) CdtProblem (81) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (82) CdtProblem (83) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (84) CdtProblem (85) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 1 ms] (86) CdtProblem (87) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (88) CdtProblem (89) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (90) CdtProblem (91) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (92) CdtProblem (93) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2 ms] (94) CdtProblem (95) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (96) CdtProblem (97) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (98) CdtProblem (99) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (100) CdtProblem (101) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (102) CdtProblem (103) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (104) CdtProblem (105) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (106) CdtProblem (107) CdtNarrowingProof [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) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (114) CdtProblem (115) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (116) CdtProblem (117) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (118) CdtProblem (119) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (120) CdtProblem (121) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (122) CdtProblem (123) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 12 ms] (124) CdtProblem (125) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (126) CdtProblem (127) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (128) CdtProblem (129) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (130) CdtProblem (131) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (132) CdtProblem (133) CdtLeafRemovalProof [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) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (140) CdtProblem (141) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (142) CdtProblem (143) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 9 ms] (144) CdtProblem (145) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (146) CdtProblem (147) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (148) CdtProblem (149) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (150) CdtProblem (151) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (152) CdtProblem (153) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (154) CdtProblem (155) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (156) CdtProblem (157) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (158) CdtProblem (159) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (160) CdtProblem (161) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (162) CdtProblem (163) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (164) CdtProblem (165) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (166) CdtProblem (167) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (168) CdtProblem (169) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (170) CdtProblem (171) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (172) CdtProblem (173) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (174) CdtProblem (175) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (176) CdtProblem (177) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (178) CdtProblem (179) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (180) CdtProblem (181) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (182) CdtProblem (183) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (184) CdtProblem (185) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (186) CdtProblem (187) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 16 ms] (188) CdtProblem (189) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (190) CdtProblem (191) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (192) CdtProblem (193) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (194) CdtProblem (195) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 12 ms] (196) CdtProblem (197) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (198) CdtProblem (199) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 21 ms] (200) CdtProblem (201) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (202) CdtProblem (203) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 23 ms] (204) CdtProblem (205) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (206) CdtProblem (207) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 47 ms] (208) CdtProblem (209) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (210) CdtProblem (211) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 18 ms] (212) CdtProblem (213) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (214) CdtProblem (215) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 52 ms] (216) CdtProblem (217) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 10 ms] (218) CdtProblem (219) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 70 ms] (220) CdtProblem (221) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (222) CdtProblem (223) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (224) CdtProblem (225) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (226) CdtProblem (227) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 56 ms] (228) CdtProblem (229) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (230) CdtProblem (231) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 30 ms] (232) CdtProblem (233) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (234) CdtProblem (235) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 67 ms] (236) CdtProblem (237) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (238) CdtProblem (239) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 57 ms] (240) CdtProblem (241) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (242) CdtProblem (243) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 27 ms] (244) CdtProblem (245) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 17 ms] (246) CdtProblem (247) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 75 ms] (248) CdtProblem (249) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (250) CdtProblem (251) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 30 ms] (252) CdtProblem (253) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (254) CdtProblem (255) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 96 ms] (256) CdtProblem (257) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (258) CdtProblem (259) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 100 ms] (260) CdtProblem (261) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 17 ms] (262) CdtProblem (263) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 27 ms] (264) CdtProblem (265) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 146 ms] (266) CdtProblem (267) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (268) CdtProblem (269) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (270) CdtProblem (271) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 121 ms] (272) CdtProblem (273) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 4 ms] (274) CdtProblem (275) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 13 ms] (276) CdtProblem (277) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 64 ms] (278) CdtProblem (279) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 4 ms] (280) CdtProblem (281) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (282) CdtProblem (283) RelTrsToWeightedTrsProof [UPPER BOUND(ID), 0 ms] (284) CpxWeightedTrs (285) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (286) CpxTypedWeightedTrs (287) CompletionProof [UPPER BOUND(ID), 3 ms] (288) CpxTypedWeightedCompleteTrs (289) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (290) CpxTypedWeightedCompleteTrs (291) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (292) CpxRNTS (293) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (294) CpxRNTS (295) CompletionProof [UPPER BOUND(ID), 0 ms] (296) CpxTypedWeightedCompleteTrs (297) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (298) CpxRNTS ---------------------------------------- (0) Obligation: The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: a__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) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT ---------------------------------------- (6) 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 ---------------------------------------- (7) CdtToCpxRelTrsProof (BOTH BOUNDS(ID, ID)) Converted S to standard rules, and D \ S as well as R to relative rules. ---------------------------------------- (8) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: A__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 The (relative) TRS S consists of the following 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 Rewrite Strategy: INNERMOST ---------------------------------------- (9) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (10) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: A__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 The (relative) TRS S consists of the following 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' Rewrite Strategy: INNERMOST ---------------------------------------- (11) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Inferred types. ---------------------------------------- (12) Obligation: Innermost TRS: Rules: 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 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' Types: A__U11 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> c:c1 tt :: tt:0':s:U11:U12:plus c :: c2:c3:c4 -> c:c1 A__U12 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> c2:c3:c4 c1 :: c:c1 c2 :: c5:c6:c7 -> c8:c9:c10:c11:c12:c13:c14 -> c2:c3:c4 A__PLUS :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> c5:c6:c7 mark :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus MARK :: tt:0':s:U11:U12:plus -> c8:c9:c10:c11:c12:c13:c14 c3 :: c5:c6:c7 -> c8:c9:c10:c11:c12:c13:c14 -> c2:c3:c4 c4 :: c2:c3:c4 0' :: tt:0':s:U11:U12:plus c5 :: c8:c9:c10:c11:c12:c13:c14 -> c5:c6:c7 s :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus c6 :: c:c1 -> c5:c6:c7 c7 :: c5:c6:c7 U11 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus c8 :: c:c1 -> c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 U12 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus c9 :: c2:c3:c4 -> c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 plus :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus c10 :: c5:c6:c7 -> c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 c11 :: c5:c6:c7 -> c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 c12 :: c8:c9:c10:c11:c12:c13:c14 c13 :: c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 c14 :: c8:c9:c10:c11:c12:c13:c14 a__U11 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus a__U12 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus a__plus :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus hole_c:c11_15 :: c:c1 hole_tt:0':s:U11:U12:plus2_15 :: tt:0':s:U11:U12:plus hole_c2:c3:c43_15 :: c2:c3:c4 hole_c5:c6:c74_15 :: c5:c6:c7 hole_c8:c9:c10:c11:c12:c13:c145_15 :: c8:c9:c10:c11:c12:c13:c14 gen_tt:0':s:U11:U12:plus6_15 :: Nat -> tt:0':s:U11:U12:plus gen_c8:c9:c10:c11:c12:c13:c147_15 :: Nat -> c8:c9:c10:c11:c12:c13:c14 ---------------------------------------- (13) OrderProof (LOWER BOUND(ID)) Heuristically decided to analyse the following defined symbols: A__U11, A__U12, A__PLUS, mark, MARK, a__U11, a__U12, a__plus They will be analysed ascendingly in the following order: A__U11 = A__U12 A__U11 = A__PLUS A__U11 = MARK A__U12 = A__PLUS mark < A__U12 A__U12 = MARK A__PLUS = MARK mark < MARK mark = a__U11 mark = a__U12 mark = a__plus a__U11 = a__U12 a__U11 = a__plus a__U12 = a__plus ---------------------------------------- (14) Obligation: Innermost TRS: Rules: 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 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' Types: A__U11 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> c:c1 tt :: tt:0':s:U11:U12:plus c :: c2:c3:c4 -> c:c1 A__U12 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> c2:c3:c4 c1 :: c:c1 c2 :: c5:c6:c7 -> c8:c9:c10:c11:c12:c13:c14 -> c2:c3:c4 A__PLUS :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> c5:c6:c7 mark :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus MARK :: tt:0':s:U11:U12:plus -> c8:c9:c10:c11:c12:c13:c14 c3 :: c5:c6:c7 -> c8:c9:c10:c11:c12:c13:c14 -> c2:c3:c4 c4 :: c2:c3:c4 0' :: tt:0':s:U11:U12:plus c5 :: c8:c9:c10:c11:c12:c13:c14 -> c5:c6:c7 s :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus c6 :: c:c1 -> c5:c6:c7 c7 :: c5:c6:c7 U11 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus c8 :: c:c1 -> c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 U12 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus c9 :: c2:c3:c4 -> c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 plus :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus c10 :: c5:c6:c7 -> c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 c11 :: c5:c6:c7 -> c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 c12 :: c8:c9:c10:c11:c12:c13:c14 c13 :: c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 c14 :: c8:c9:c10:c11:c12:c13:c14 a__U11 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus a__U12 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus a__plus :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus hole_c:c11_15 :: c:c1 hole_tt:0':s:U11:U12:plus2_15 :: tt:0':s:U11:U12:plus hole_c2:c3:c43_15 :: c2:c3:c4 hole_c5:c6:c74_15 :: c5:c6:c7 hole_c8:c9:c10:c11:c12:c13:c145_15 :: c8:c9:c10:c11:c12:c13:c14 gen_tt:0':s:U11:U12:plus6_15 :: Nat -> tt:0':s:U11:U12:plus gen_c8:c9:c10:c11:c12:c13:c147_15 :: Nat -> c8:c9:c10:c11:c12:c13:c14 Generator Equations: gen_tt:0':s:U11:U12:plus6_15(0) <=> tt gen_tt:0':s:U11:U12:plus6_15(+(x, 1)) <=> s(gen_tt:0':s:U11:U12:plus6_15(x)) gen_c8:c9:c10:c11:c12:c13:c147_15(0) <=> c12 gen_c8:c9:c10:c11:c12:c13:c147_15(+(x, 1)) <=> c8(c(c2(c5(c12), c12)), gen_c8:c9:c10:c11:c12:c13:c147_15(x)) The following defined symbols remain to be analysed: a__U11, A__U11, A__U12, A__PLUS, mark, MARK, a__U12, a__plus They will be analysed ascendingly in the following order: A__U11 = A__U12 A__U11 = A__PLUS A__U11 = MARK A__U12 = A__PLUS mark < A__U12 A__U12 = MARK A__PLUS = MARK mark < MARK mark = a__U11 mark = a__U12 mark = a__plus a__U11 = a__U12 a__U11 = a__plus a__U12 = a__plus ---------------------------------------- (15) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: mark(gen_tt:0':s:U11:U12:plus6_15(n12226_15)) -> gen_tt:0':s:U11:U12:plus6_15(n12226_15), rt in Omega(0) Induction Base: mark(gen_tt:0':s:U11:U12:plus6_15(0)) ->_R^Omega(0) tt Induction Step: mark(gen_tt:0':s:U11:U12:plus6_15(+(n12226_15, 1))) ->_R^Omega(0) s(mark(gen_tt:0':s:U11:U12:plus6_15(n12226_15))) ->_IH s(gen_tt:0':s:U11:U12:plus6_15(c12227_15)) We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0). ---------------------------------------- (16) Obligation: Innermost TRS: Rules: A__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 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' Types: A__U11 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> c:c1 tt :: tt:0':s:U11:U12:plus c :: c2:c3:c4 -> c:c1 A__U12 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> c2:c3:c4 c1 :: c:c1 c2 :: c5:c6:c7 -> c8:c9:c10:c11:c12:c13:c14 -> c2:c3:c4 A__PLUS :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> c5:c6:c7 mark :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus MARK :: tt:0':s:U11:U12:plus -> c8:c9:c10:c11:c12:c13:c14 c3 :: c5:c6:c7 -> c8:c9:c10:c11:c12:c13:c14 -> c2:c3:c4 c4 :: c2:c3:c4 0' :: tt:0':s:U11:U12:plus c5 :: c8:c9:c10:c11:c12:c13:c14 -> c5:c6:c7 s :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus c6 :: c:c1 -> c5:c6:c7 c7 :: c5:c6:c7 U11 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus c8 :: c:c1 -> c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 U12 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus c9 :: c2:c3:c4 -> c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 plus :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus c10 :: c5:c6:c7 -> c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 c11 :: c5:c6:c7 -> c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 c12 :: c8:c9:c10:c11:c12:c13:c14 c13 :: c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 c14 :: c8:c9:c10:c11:c12:c13:c14 a__U11 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus a__U12 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus a__plus :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus hole_c:c11_15 :: c:c1 hole_tt:0':s:U11:U12:plus2_15 :: tt:0':s:U11:U12:plus hole_c2:c3:c43_15 :: c2:c3:c4 hole_c5:c6:c74_15 :: c5:c6:c7 hole_c8:c9:c10:c11:c12:c13:c145_15 :: c8:c9:c10:c11:c12:c13:c14 gen_tt:0':s:U11:U12:plus6_15 :: Nat -> tt:0':s:U11:U12:plus gen_c8:c9:c10:c11:c12:c13:c147_15 :: Nat -> c8:c9:c10:c11:c12:c13:c14 Lemmas: mark(gen_tt:0':s:U11:U12:plus6_15(n12226_15)) -> gen_tt:0':s:U11:U12:plus6_15(n12226_15), rt in Omega(0) Generator Equations: gen_tt:0':s:U11:U12:plus6_15(0) <=> tt gen_tt:0':s:U11:U12:plus6_15(+(x, 1)) <=> s(gen_tt:0':s:U11:U12:plus6_15(x)) gen_c8:c9:c10:c11:c12:c13:c147_15(0) <=> c12 gen_c8:c9:c10:c11:c12:c13:c147_15(+(x, 1)) <=> c8(c(c2(c5(c12), c12)), gen_c8:c9:c10:c11:c12:c13:c147_15(x)) The following defined symbols remain to be analysed: a__U11, A__U11, A__U12, A__PLUS, MARK, a__U12, a__plus They will be analysed ascendingly in the following order: A__U11 = A__U12 A__U11 = A__PLUS A__U11 = MARK A__U12 = A__PLUS mark < A__U12 A__U12 = MARK A__PLUS = MARK mark < MARK mark = a__U11 mark = a__U12 mark = a__plus a__U11 = a__U12 a__U11 = a__plus a__U12 = a__plus ---------------------------------------- (17) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: a__U11(gen_tt:0':s:U11:U12:plus6_15(0), gen_tt:0':s:U11:U12:plus6_15(n13042_15), gen_tt:0':s:U11:U12:plus6_15(c)) -> *8_15, rt in Omega(0) Induction Base: a__U11(gen_tt:0':s:U11:U12:plus6_15(0), gen_tt:0':s:U11:U12:plus6_15(0), gen_tt:0':s:U11:U12:plus6_15(c)) Induction Step: a__U11(gen_tt:0':s:U11:U12:plus6_15(0), gen_tt:0':s:U11:U12:plus6_15(+(n13042_15, 1)), gen_tt:0':s:U11:U12:plus6_15(c)) ->_R^Omega(0) a__U12(tt, gen_tt:0':s:U11:U12:plus6_15(+(n13042_15, 1)), gen_tt:0':s:U11:U12:plus6_15(c)) ->_R^Omega(0) s(a__plus(mark(gen_tt:0':s:U11:U12:plus6_15(c)), mark(gen_tt:0':s:U11:U12:plus6_15(+(1, n13042_15))))) ->_L^Omega(0) s(a__plus(gen_tt:0':s:U11:U12:plus6_15(c), mark(gen_tt:0':s:U11:U12:plus6_15(+(1, n13042_15))))) ->_L^Omega(0) s(a__plus(gen_tt:0':s:U11:U12:plus6_15(c), gen_tt:0':s:U11:U12:plus6_15(+(1, n13042_15)))) ->_R^Omega(0) s(a__U11(tt, gen_tt:0':s:U11:U12:plus6_15(n13042_15), gen_tt:0':s:U11:U12:plus6_15(c))) ->_IH s(*8_15) We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0). ---------------------------------------- (18) Obligation: Innermost TRS: Rules: A__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 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' Types: A__U11 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> c:c1 tt :: tt:0':s:U11:U12:plus c :: c2:c3:c4 -> c:c1 A__U12 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> c2:c3:c4 c1 :: c:c1 c2 :: c5:c6:c7 -> c8:c9:c10:c11:c12:c13:c14 -> c2:c3:c4 A__PLUS :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> c5:c6:c7 mark :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus MARK :: tt:0':s:U11:U12:plus -> c8:c9:c10:c11:c12:c13:c14 c3 :: c5:c6:c7 -> c8:c9:c10:c11:c12:c13:c14 -> c2:c3:c4 c4 :: c2:c3:c4 0' :: tt:0':s:U11:U12:plus c5 :: c8:c9:c10:c11:c12:c13:c14 -> c5:c6:c7 s :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus c6 :: c:c1 -> c5:c6:c7 c7 :: c5:c6:c7 U11 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus c8 :: c:c1 -> c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 U12 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus c9 :: c2:c3:c4 -> c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 plus :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus c10 :: c5:c6:c7 -> c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 c11 :: c5:c6:c7 -> c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 c12 :: c8:c9:c10:c11:c12:c13:c14 c13 :: c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 c14 :: c8:c9:c10:c11:c12:c13:c14 a__U11 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus a__U12 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus a__plus :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus hole_c:c11_15 :: c:c1 hole_tt:0':s:U11:U12:plus2_15 :: tt:0':s:U11:U12:plus hole_c2:c3:c43_15 :: c2:c3:c4 hole_c5:c6:c74_15 :: c5:c6:c7 hole_c8:c9:c10:c11:c12:c13:c145_15 :: c8:c9:c10:c11:c12:c13:c14 gen_tt:0':s:U11:U12:plus6_15 :: Nat -> tt:0':s:U11:U12:plus gen_c8:c9:c10:c11:c12:c13:c147_15 :: Nat -> c8:c9:c10:c11:c12:c13:c14 Lemmas: mark(gen_tt:0':s:U11:U12:plus6_15(n12226_15)) -> gen_tt:0':s:U11:U12:plus6_15(n12226_15), rt in Omega(0) a__U11(gen_tt:0':s:U11:U12:plus6_15(0), gen_tt:0':s:U11:U12:plus6_15(n13042_15), gen_tt:0':s:U11:U12:plus6_15(c)) -> *8_15, rt in Omega(0) Generator Equations: gen_tt:0':s:U11:U12:plus6_15(0) <=> tt gen_tt:0':s:U11:U12:plus6_15(+(x, 1)) <=> s(gen_tt:0':s:U11:U12:plus6_15(x)) gen_c8:c9:c10:c11:c12:c13:c147_15(0) <=> c12 gen_c8:c9:c10:c11:c12:c13:c147_15(+(x, 1)) <=> c8(c(c2(c5(c12), c12)), gen_c8:c9:c10:c11:c12:c13:c147_15(x)) The following defined symbols remain to be analysed: a__U12, A__U11, A__U12, A__PLUS, mark, MARK, a__plus They will be analysed ascendingly in the following order: A__U11 = A__U12 A__U11 = A__PLUS A__U11 = MARK A__U12 = A__PLUS mark < A__U12 A__U12 = MARK A__PLUS = MARK mark < MARK mark = a__U11 mark = a__U12 mark = a__plus a__U11 = a__U12 a__U11 = a__plus a__U12 = a__plus ---------------------------------------- (19) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: a__U12(gen_tt:0':s:U11:U12:plus6_15(0), gen_tt:0':s:U11:U12:plus6_15(n17566_15), gen_tt:0':s:U11:U12:plus6_15(c)) -> *8_15, rt in Omega(0) Induction Base: a__U12(gen_tt:0':s:U11:U12:plus6_15(0), gen_tt:0':s:U11:U12:plus6_15(0), gen_tt:0':s:U11:U12:plus6_15(c)) Induction Step: a__U12(gen_tt:0':s:U11:U12:plus6_15(0), gen_tt:0':s:U11:U12:plus6_15(+(n17566_15, 1)), gen_tt:0':s:U11:U12:plus6_15(c)) ->_R^Omega(0) s(a__plus(mark(gen_tt:0':s:U11:U12:plus6_15(c)), mark(gen_tt:0':s:U11:U12:plus6_15(+(n17566_15, 1))))) ->_L^Omega(0) s(a__plus(gen_tt:0':s:U11:U12:plus6_15(c), mark(gen_tt:0':s:U11:U12:plus6_15(+(1, n17566_15))))) ->_L^Omega(0) s(a__plus(gen_tt:0':s:U11:U12:plus6_15(c), gen_tt:0':s:U11:U12:plus6_15(+(1, n17566_15)))) ->_R^Omega(0) s(a__U11(tt, gen_tt:0':s:U11:U12:plus6_15(n17566_15), gen_tt:0':s:U11:U12:plus6_15(c))) ->_R^Omega(0) s(a__U12(tt, gen_tt:0':s:U11:U12:plus6_15(n17566_15), gen_tt:0':s:U11:U12:plus6_15(c))) ->_IH s(*8_15) We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0). ---------------------------------------- (20) Obligation: Innermost TRS: Rules: A__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 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' Types: A__U11 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> c:c1 tt :: tt:0':s:U11:U12:plus c :: c2:c3:c4 -> c:c1 A__U12 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> c2:c3:c4 c1 :: c:c1 c2 :: c5:c6:c7 -> c8:c9:c10:c11:c12:c13:c14 -> c2:c3:c4 A__PLUS :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> c5:c6:c7 mark :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus MARK :: tt:0':s:U11:U12:plus -> c8:c9:c10:c11:c12:c13:c14 c3 :: c5:c6:c7 -> c8:c9:c10:c11:c12:c13:c14 -> c2:c3:c4 c4 :: c2:c3:c4 0' :: tt:0':s:U11:U12:plus c5 :: c8:c9:c10:c11:c12:c13:c14 -> c5:c6:c7 s :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus c6 :: c:c1 -> c5:c6:c7 c7 :: c5:c6:c7 U11 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus c8 :: c:c1 -> c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 U12 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus c9 :: c2:c3:c4 -> c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 plus :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus c10 :: c5:c6:c7 -> c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 c11 :: c5:c6:c7 -> c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 c12 :: c8:c9:c10:c11:c12:c13:c14 c13 :: c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 c14 :: c8:c9:c10:c11:c12:c13:c14 a__U11 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus a__U12 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus a__plus :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus hole_c:c11_15 :: c:c1 hole_tt:0':s:U11:U12:plus2_15 :: tt:0':s:U11:U12:plus hole_c2:c3:c43_15 :: c2:c3:c4 hole_c5:c6:c74_15 :: c5:c6:c7 hole_c8:c9:c10:c11:c12:c13:c145_15 :: c8:c9:c10:c11:c12:c13:c14 gen_tt:0':s:U11:U12:plus6_15 :: Nat -> tt:0':s:U11:U12:plus gen_c8:c9:c10:c11:c12:c13:c147_15 :: Nat -> c8:c9:c10:c11:c12:c13:c14 Lemmas: mark(gen_tt:0':s:U11:U12:plus6_15(n12226_15)) -> gen_tt:0':s:U11:U12:plus6_15(n12226_15), rt in Omega(0) a__U11(gen_tt:0':s:U11:U12:plus6_15(0), gen_tt:0':s:U11:U12:plus6_15(n13042_15), gen_tt:0':s:U11:U12:plus6_15(c)) -> *8_15, rt in Omega(0) a__U12(gen_tt:0':s:U11:U12:plus6_15(0), gen_tt:0':s:U11:U12:plus6_15(n17566_15), gen_tt:0':s:U11:U12:plus6_15(c)) -> *8_15, rt in Omega(0) Generator Equations: gen_tt:0':s:U11:U12:plus6_15(0) <=> tt gen_tt:0':s:U11:U12:plus6_15(+(x, 1)) <=> s(gen_tt:0':s:U11:U12:plus6_15(x)) gen_c8:c9:c10:c11:c12:c13:c147_15(0) <=> c12 gen_c8:c9:c10:c11:c12:c13:c147_15(+(x, 1)) <=> c8(c(c2(c5(c12), c12)), gen_c8:c9:c10:c11:c12:c13:c147_15(x)) The following defined symbols remain to be analysed: a__plus, A__U11, A__U12, A__PLUS, mark, MARK, a__U11 They will be analysed ascendingly in the following order: A__U11 = A__U12 A__U11 = A__PLUS A__U11 = MARK A__U12 = A__PLUS mark < A__U12 A__U12 = MARK A__PLUS = MARK mark < MARK mark = a__U11 mark = a__U12 mark = a__plus a__U11 = a__U12 a__U11 = a__plus a__U12 = a__plus ---------------------------------------- (21) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: a__plus(gen_tt:0':s:U11:U12:plus6_15(a), gen_tt:0':s:U11:U12:plus6_15(+(1, n22156_15))) -> *8_15, rt in Omega(0) Induction Base: a__plus(gen_tt:0':s:U11:U12:plus6_15(a), gen_tt:0':s:U11:U12:plus6_15(+(1, 0))) Induction Step: a__plus(gen_tt:0':s:U11:U12:plus6_15(a), gen_tt:0':s:U11:U12:plus6_15(+(1, +(n22156_15, 1)))) ->_R^Omega(0) a__U11(tt, gen_tt:0':s:U11:U12:plus6_15(+(1, n22156_15)), gen_tt:0':s:U11:U12:plus6_15(a)) ->_R^Omega(0) a__U12(tt, gen_tt:0':s:U11:U12:plus6_15(+(1, n22156_15)), gen_tt:0':s:U11:U12:plus6_15(a)) ->_R^Omega(0) s(a__plus(mark(gen_tt:0':s:U11:U12:plus6_15(a)), mark(gen_tt:0':s:U11:U12:plus6_15(+(1, n22156_15))))) ->_L^Omega(0) s(a__plus(gen_tt:0':s:U11:U12:plus6_15(a), mark(gen_tt:0':s:U11:U12:plus6_15(+(1, n22156_15))))) ->_L^Omega(0) s(a__plus(gen_tt:0':s:U11:U12:plus6_15(a), gen_tt:0':s:U11:U12:plus6_15(+(1, n22156_15)))) ->_IH s(*8_15) We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0). ---------------------------------------- (22) Obligation: Innermost TRS: Rules: A__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 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' Types: A__U11 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> c:c1 tt :: tt:0':s:U11:U12:plus c :: c2:c3:c4 -> c:c1 A__U12 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> c2:c3:c4 c1 :: c:c1 c2 :: c5:c6:c7 -> c8:c9:c10:c11:c12:c13:c14 -> c2:c3:c4 A__PLUS :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> c5:c6:c7 mark :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus MARK :: tt:0':s:U11:U12:plus -> c8:c9:c10:c11:c12:c13:c14 c3 :: c5:c6:c7 -> c8:c9:c10:c11:c12:c13:c14 -> c2:c3:c4 c4 :: c2:c3:c4 0' :: tt:0':s:U11:U12:plus c5 :: c8:c9:c10:c11:c12:c13:c14 -> c5:c6:c7 s :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus c6 :: c:c1 -> c5:c6:c7 c7 :: c5:c6:c7 U11 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus c8 :: c:c1 -> c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 U12 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus c9 :: c2:c3:c4 -> c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 plus :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus c10 :: c5:c6:c7 -> c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 c11 :: c5:c6:c7 -> c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 c12 :: c8:c9:c10:c11:c12:c13:c14 c13 :: c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 c14 :: c8:c9:c10:c11:c12:c13:c14 a__U11 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus a__U12 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus a__plus :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus hole_c:c11_15 :: c:c1 hole_tt:0':s:U11:U12:plus2_15 :: tt:0':s:U11:U12:plus hole_c2:c3:c43_15 :: c2:c3:c4 hole_c5:c6:c74_15 :: c5:c6:c7 hole_c8:c9:c10:c11:c12:c13:c145_15 :: c8:c9:c10:c11:c12:c13:c14 gen_tt:0':s:U11:U12:plus6_15 :: Nat -> tt:0':s:U11:U12:plus gen_c8:c9:c10:c11:c12:c13:c147_15 :: Nat -> c8:c9:c10:c11:c12:c13:c14 Lemmas: mark(gen_tt:0':s:U11:U12:plus6_15(n12226_15)) -> gen_tt:0':s:U11:U12:plus6_15(n12226_15), rt in Omega(0) a__U11(gen_tt:0':s:U11:U12:plus6_15(0), gen_tt:0':s:U11:U12:plus6_15(n13042_15), gen_tt:0':s:U11:U12:plus6_15(c)) -> *8_15, rt in Omega(0) a__U12(gen_tt:0':s:U11:U12:plus6_15(0), gen_tt:0':s:U11:U12:plus6_15(n17566_15), gen_tt:0':s:U11:U12:plus6_15(c)) -> *8_15, rt in Omega(0) a__plus(gen_tt:0':s:U11:U12:plus6_15(a), gen_tt:0':s:U11:U12:plus6_15(+(1, n22156_15))) -> *8_15, rt in Omega(0) Generator Equations: gen_tt:0':s:U11:U12:plus6_15(0) <=> tt gen_tt:0':s:U11:U12:plus6_15(+(x, 1)) <=> s(gen_tt:0':s:U11:U12:plus6_15(x)) gen_c8:c9:c10:c11:c12:c13:c147_15(0) <=> c12 gen_c8:c9:c10:c11:c12:c13:c147_15(+(x, 1)) <=> c8(c(c2(c5(c12), c12)), gen_c8:c9:c10:c11:c12:c13:c147_15(x)) The following defined symbols remain to be analysed: mark, A__U11, A__U12, A__PLUS, MARK, a__U11, a__U12 They will be analysed ascendingly in the following order: A__U11 = A__U12 A__U11 = A__PLUS A__U11 = MARK A__U12 = A__PLUS mark < A__U12 A__U12 = MARK A__PLUS = MARK mark < MARK mark = a__U11 mark = a__U12 mark = a__plus a__U11 = a__U12 a__U11 = a__plus a__U12 = a__plus ---------------------------------------- (23) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: mark(gen_tt:0':s:U11:U12:plus6_15(n27715_15)) -> gen_tt:0':s:U11:U12:plus6_15(n27715_15), rt in Omega(0) Induction Base: mark(gen_tt:0':s:U11:U12:plus6_15(0)) ->_R^Omega(0) tt Induction Step: mark(gen_tt:0':s:U11:U12:plus6_15(+(n27715_15, 1))) ->_R^Omega(0) s(mark(gen_tt:0':s:U11:U12:plus6_15(n27715_15))) ->_IH s(gen_tt:0':s:U11:U12:plus6_15(c27716_15)) We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0). ---------------------------------------- (24) Obligation: Innermost TRS: Rules: A__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 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' Types: A__U11 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> c:c1 tt :: tt:0':s:U11:U12:plus c :: c2:c3:c4 -> c:c1 A__U12 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> c2:c3:c4 c1 :: c:c1 c2 :: c5:c6:c7 -> c8:c9:c10:c11:c12:c13:c14 -> c2:c3:c4 A__PLUS :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> c5:c6:c7 mark :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus MARK :: tt:0':s:U11:U12:plus -> c8:c9:c10:c11:c12:c13:c14 c3 :: c5:c6:c7 -> c8:c9:c10:c11:c12:c13:c14 -> c2:c3:c4 c4 :: c2:c3:c4 0' :: tt:0':s:U11:U12:plus c5 :: c8:c9:c10:c11:c12:c13:c14 -> c5:c6:c7 s :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus c6 :: c:c1 -> c5:c6:c7 c7 :: c5:c6:c7 U11 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus c8 :: c:c1 -> c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 U12 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus c9 :: c2:c3:c4 -> c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 plus :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus c10 :: c5:c6:c7 -> c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 c11 :: c5:c6:c7 -> c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 c12 :: c8:c9:c10:c11:c12:c13:c14 c13 :: c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 c14 :: c8:c9:c10:c11:c12:c13:c14 a__U11 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus a__U12 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus a__plus :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus hole_c:c11_15 :: c:c1 hole_tt:0':s:U11:U12:plus2_15 :: tt:0':s:U11:U12:plus hole_c2:c3:c43_15 :: c2:c3:c4 hole_c5:c6:c74_15 :: c5:c6:c7 hole_c8:c9:c10:c11:c12:c13:c145_15 :: c8:c9:c10:c11:c12:c13:c14 gen_tt:0':s:U11:U12:plus6_15 :: Nat -> tt:0':s:U11:U12:plus gen_c8:c9:c10:c11:c12:c13:c147_15 :: Nat -> c8:c9:c10:c11:c12:c13:c14 Lemmas: mark(gen_tt:0':s:U11:U12:plus6_15(n27715_15)) -> gen_tt:0':s:U11:U12:plus6_15(n27715_15), rt in Omega(0) a__U11(gen_tt:0':s:U11:U12:plus6_15(0), gen_tt:0':s:U11:U12:plus6_15(n13042_15), gen_tt:0':s:U11:U12:plus6_15(c)) -> *8_15, rt in Omega(0) a__U12(gen_tt:0':s:U11:U12:plus6_15(0), gen_tt:0':s:U11:U12:plus6_15(n17566_15), gen_tt:0':s:U11:U12:plus6_15(c)) -> *8_15, rt in Omega(0) a__plus(gen_tt:0':s:U11:U12:plus6_15(a), gen_tt:0':s:U11:U12:plus6_15(+(1, n22156_15))) -> *8_15, rt in Omega(0) Generator Equations: gen_tt:0':s:U11:U12:plus6_15(0) <=> tt gen_tt:0':s:U11:U12:plus6_15(+(x, 1)) <=> s(gen_tt:0':s:U11:U12:plus6_15(x)) gen_c8:c9:c10:c11:c12:c13:c147_15(0) <=> c12 gen_c8:c9:c10:c11:c12:c13:c147_15(+(x, 1)) <=> c8(c(c2(c5(c12), c12)), gen_c8:c9:c10:c11:c12:c13:c147_15(x)) The following defined symbols remain to be analysed: a__U11, A__U11, A__U12, A__PLUS, MARK, a__U12 They will be analysed ascendingly in the following order: A__U11 = A__U12 A__U11 = A__PLUS A__U11 = MARK A__U12 = A__PLUS mark < A__U12 A__U12 = MARK A__PLUS = MARK mark < MARK mark = a__U11 mark = a__U12 mark = a__plus a__U11 = a__U12 a__U11 = a__plus a__U12 = a__plus ---------------------------------------- (25) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: a__U11(gen_tt:0':s:U11:U12:plus6_15(0), gen_tt:0':s:U11:U12:plus6_15(n28840_15), gen_tt:0':s:U11:U12:plus6_15(c)) -> *8_15, rt in Omega(0) Induction Base: a__U11(gen_tt:0':s:U11:U12:plus6_15(0), gen_tt:0':s:U11:U12:plus6_15(0), gen_tt:0':s:U11:U12:plus6_15(c)) Induction Step: a__U11(gen_tt:0':s:U11:U12:plus6_15(0), gen_tt:0':s:U11:U12:plus6_15(+(n28840_15, 1)), gen_tt:0':s:U11:U12:plus6_15(c)) ->_R^Omega(0) a__U12(tt, gen_tt:0':s:U11:U12:plus6_15(+(n28840_15, 1)), gen_tt:0':s:U11:U12:plus6_15(c)) ->_R^Omega(0) s(a__plus(mark(gen_tt:0':s:U11:U12:plus6_15(c)), mark(gen_tt:0':s:U11:U12:plus6_15(+(1, n28840_15))))) ->_L^Omega(0) s(a__plus(gen_tt:0':s:U11:U12:plus6_15(c), mark(gen_tt:0':s:U11:U12:plus6_15(+(1, n28840_15))))) ->_L^Omega(0) s(a__plus(gen_tt:0':s:U11:U12:plus6_15(c), gen_tt:0':s:U11:U12:plus6_15(+(1, n28840_15)))) ->_R^Omega(0) s(a__U11(tt, gen_tt:0':s:U11:U12:plus6_15(n28840_15), gen_tt:0':s:U11:U12:plus6_15(c))) ->_IH s(*8_15) We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0). ---------------------------------------- (26) Obligation: Innermost TRS: Rules: 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 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' Types: A__U11 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> c:c1 tt :: tt:0':s:U11:U12:plus c :: c2:c3:c4 -> c:c1 A__U12 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> c2:c3:c4 c1 :: c:c1 c2 :: c5:c6:c7 -> c8:c9:c10:c11:c12:c13:c14 -> c2:c3:c4 A__PLUS :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> c5:c6:c7 mark :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus MARK :: tt:0':s:U11:U12:plus -> c8:c9:c10:c11:c12:c13:c14 c3 :: c5:c6:c7 -> c8:c9:c10:c11:c12:c13:c14 -> c2:c3:c4 c4 :: c2:c3:c4 0' :: tt:0':s:U11:U12:plus c5 :: c8:c9:c10:c11:c12:c13:c14 -> c5:c6:c7 s :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus c6 :: c:c1 -> c5:c6:c7 c7 :: c5:c6:c7 U11 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus c8 :: c:c1 -> c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 U12 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus c9 :: c2:c3:c4 -> c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 plus :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus c10 :: c5:c6:c7 -> c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 c11 :: c5:c6:c7 -> c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 c12 :: c8:c9:c10:c11:c12:c13:c14 c13 :: c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 c14 :: c8:c9:c10:c11:c12:c13:c14 a__U11 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus a__U12 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus a__plus :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus hole_c:c11_15 :: c:c1 hole_tt:0':s:U11:U12:plus2_15 :: tt:0':s:U11:U12:plus hole_c2:c3:c43_15 :: c2:c3:c4 hole_c5:c6:c74_15 :: c5:c6:c7 hole_c8:c9:c10:c11:c12:c13:c145_15 :: c8:c9:c10:c11:c12:c13:c14 gen_tt:0':s:U11:U12:plus6_15 :: Nat -> tt:0':s:U11:U12:plus gen_c8:c9:c10:c11:c12:c13:c147_15 :: Nat -> c8:c9:c10:c11:c12:c13:c14 Lemmas: mark(gen_tt:0':s:U11:U12:plus6_15(n27715_15)) -> gen_tt:0':s:U11:U12:plus6_15(n27715_15), rt in Omega(0) a__U11(gen_tt:0':s:U11:U12:plus6_15(0), gen_tt:0':s:U11:U12:plus6_15(n28840_15), gen_tt:0':s:U11:U12:plus6_15(c)) -> *8_15, rt in Omega(0) a__U12(gen_tt:0':s:U11:U12:plus6_15(0), gen_tt:0':s:U11:U12:plus6_15(n17566_15), gen_tt:0':s:U11:U12:plus6_15(c)) -> *8_15, rt in Omega(0) a__plus(gen_tt:0':s:U11:U12:plus6_15(a), gen_tt:0':s:U11:U12:plus6_15(+(1, n22156_15))) -> *8_15, rt in Omega(0) Generator Equations: gen_tt:0':s:U11:U12:plus6_15(0) <=> tt gen_tt:0':s:U11:U12:plus6_15(+(x, 1)) <=> s(gen_tt:0':s:U11:U12:plus6_15(x)) gen_c8:c9:c10:c11:c12:c13:c147_15(0) <=> c12 gen_c8:c9:c10:c11:c12:c13:c147_15(+(x, 1)) <=> c8(c(c2(c5(c12), c12)), gen_c8:c9:c10:c11:c12:c13:c147_15(x)) The following defined symbols remain to be analysed: a__U12, A__U11, A__U12, A__PLUS, MARK They will be analysed ascendingly in the following order: A__U11 = A__U12 A__U11 = A__PLUS A__U11 = MARK A__U12 = A__PLUS mark < A__U12 A__U12 = MARK A__PLUS = MARK mark < MARK mark = a__U11 mark = a__U12 mark = a__plus a__U11 = a__U12 a__U11 = a__plus a__U12 = a__plus ---------------------------------------- (27) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: a__U12(gen_tt:0':s:U11:U12:plus6_15(0), gen_tt:0':s:U11:U12:plus6_15(n34579_15), gen_tt:0':s:U11:U12:plus6_15(c)) -> *8_15, rt in Omega(0) Induction Base: a__U12(gen_tt:0':s:U11:U12:plus6_15(0), gen_tt:0':s:U11:U12:plus6_15(0), gen_tt:0':s:U11:U12:plus6_15(c)) Induction Step: a__U12(gen_tt:0':s:U11:U12:plus6_15(0), gen_tt:0':s:U11:U12:plus6_15(+(n34579_15, 1)), gen_tt:0':s:U11:U12:plus6_15(c)) ->_R^Omega(0) s(a__plus(mark(gen_tt:0':s:U11:U12:plus6_15(c)), mark(gen_tt:0':s:U11:U12:plus6_15(+(n34579_15, 1))))) ->_L^Omega(0) s(a__plus(gen_tt:0':s:U11:U12:plus6_15(c), mark(gen_tt:0':s:U11:U12:plus6_15(+(1, n34579_15))))) ->_L^Omega(0) s(a__plus(gen_tt:0':s:U11:U12:plus6_15(c), gen_tt:0':s:U11:U12:plus6_15(+(1, n34579_15)))) ->_R^Omega(0) s(a__U11(tt, gen_tt:0':s:U11:U12:plus6_15(n34579_15), gen_tt:0':s:U11:U12:plus6_15(c))) ->_R^Omega(0) s(a__U12(tt, gen_tt:0':s:U11:U12:plus6_15(n34579_15), gen_tt:0':s:U11:U12:plus6_15(c))) ->_IH s(*8_15) We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0). ---------------------------------------- (28) Obligation: Innermost TRS: Rules: 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 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' Types: A__U11 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> c:c1 tt :: tt:0':s:U11:U12:plus c :: c2:c3:c4 -> c:c1 A__U12 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> c2:c3:c4 c1 :: c:c1 c2 :: c5:c6:c7 -> c8:c9:c10:c11:c12:c13:c14 -> c2:c3:c4 A__PLUS :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> c5:c6:c7 mark :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus MARK :: tt:0':s:U11:U12:plus -> c8:c9:c10:c11:c12:c13:c14 c3 :: c5:c6:c7 -> c8:c9:c10:c11:c12:c13:c14 -> c2:c3:c4 c4 :: c2:c3:c4 0' :: tt:0':s:U11:U12:plus c5 :: c8:c9:c10:c11:c12:c13:c14 -> c5:c6:c7 s :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus c6 :: c:c1 -> c5:c6:c7 c7 :: c5:c6:c7 U11 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus c8 :: c:c1 -> c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 U12 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus c9 :: c2:c3:c4 -> c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 plus :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus c10 :: c5:c6:c7 -> c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 c11 :: c5:c6:c7 -> c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 c12 :: c8:c9:c10:c11:c12:c13:c14 c13 :: c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 c14 :: c8:c9:c10:c11:c12:c13:c14 a__U11 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus a__U12 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus a__plus :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus hole_c:c11_15 :: c:c1 hole_tt:0':s:U11:U12:plus2_15 :: tt:0':s:U11:U12:plus hole_c2:c3:c43_15 :: c2:c3:c4 hole_c5:c6:c74_15 :: c5:c6:c7 hole_c8:c9:c10:c11:c12:c13:c145_15 :: c8:c9:c10:c11:c12:c13:c14 gen_tt:0':s:U11:U12:plus6_15 :: Nat -> tt:0':s:U11:U12:plus gen_c8:c9:c10:c11:c12:c13:c147_15 :: Nat -> c8:c9:c10:c11:c12:c13:c14 Lemmas: mark(gen_tt:0':s:U11:U12:plus6_15(n27715_15)) -> gen_tt:0':s:U11:U12:plus6_15(n27715_15), rt in Omega(0) a__U11(gen_tt:0':s:U11:U12:plus6_15(0), gen_tt:0':s:U11:U12:plus6_15(n28840_15), gen_tt:0':s:U11:U12:plus6_15(c)) -> *8_15, rt in Omega(0) a__U12(gen_tt:0':s:U11:U12:plus6_15(0), gen_tt:0':s:U11:U12:plus6_15(n34579_15), gen_tt:0':s:U11:U12:plus6_15(c)) -> *8_15, rt in Omega(0) a__plus(gen_tt:0':s:U11:U12:plus6_15(a), gen_tt:0':s:U11:U12:plus6_15(+(1, n22156_15))) -> *8_15, rt in Omega(0) Generator Equations: gen_tt:0':s:U11:U12:plus6_15(0) <=> tt gen_tt:0':s:U11:U12:plus6_15(+(x, 1)) <=> s(gen_tt:0':s:U11:U12:plus6_15(x)) gen_c8:c9:c10:c11:c12:c13:c147_15(0) <=> c12 gen_c8:c9:c10:c11:c12:c13:c147_15(+(x, 1)) <=> c8(c(c2(c5(c12), c12)), gen_c8:c9:c10:c11:c12:c13:c147_15(x)) The following defined symbols remain to be analysed: A__U12, A__U11, A__PLUS, MARK They will be analysed ascendingly in the following order: A__U11 = A__U12 A__U11 = A__PLUS A__U11 = MARK A__U12 = A__PLUS A__U12 = MARK A__PLUS = MARK ---------------------------------------- (29) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: A__U12(gen_tt:0':s:U11:U12:plus6_15(0), gen_tt:0':s:U11:U12:plus6_15(n39961_15), gen_tt:0':s:U11:U12:plus6_15(c)) -> *8_15, rt in Omega(n39961_15) Induction Base: A__U12(gen_tt:0':s:U11:U12:plus6_15(0), gen_tt:0':s:U11:U12:plus6_15(0), gen_tt:0':s:U11:U12:plus6_15(c)) Induction Step: A__U12(gen_tt:0':s:U11:U12:plus6_15(0), gen_tt:0':s:U11:U12:plus6_15(+(n39961_15, 1)), gen_tt:0':s:U11:U12:plus6_15(c)) ->_R^Omega(1) c2(A__PLUS(mark(gen_tt:0':s:U11:U12:plus6_15(c)), mark(gen_tt:0':s:U11:U12:plus6_15(+(n39961_15, 1)))), MARK(gen_tt:0':s:U11:U12:plus6_15(c))) ->_L^Omega(0) c2(A__PLUS(gen_tt:0':s:U11:U12:plus6_15(c), mark(gen_tt:0':s:U11:U12:plus6_15(+(1, n39961_15)))), MARK(gen_tt:0':s:U11:U12:plus6_15(c))) ->_L^Omega(0) c2(A__PLUS(gen_tt:0':s:U11:U12:plus6_15(c), gen_tt:0':s:U11:U12:plus6_15(+(1, n39961_15))), MARK(gen_tt:0':s:U11:U12:plus6_15(c))) ->_R^Omega(1) c2(c6(A__U11(tt, gen_tt:0':s:U11:U12:plus6_15(n39961_15), gen_tt:0':s:U11:U12:plus6_15(c))), MARK(gen_tt:0':s:U11:U12:plus6_15(c))) ->_R^Omega(1) c2(c6(c(A__U12(tt, gen_tt:0':s:U11:U12:plus6_15(n39961_15), gen_tt:0':s:U11:U12:plus6_15(c)))), MARK(gen_tt:0':s:U11:U12:plus6_15(c))) ->_IH c2(c6(c(*8_15)), MARK(gen_tt:0':s:U11:U12:plus6_15(c))) We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). ---------------------------------------- (30) Complex Obligation (BEST) ---------------------------------------- (31) Obligation: Proved the lower bound n^1 for the following obligation: Innermost TRS: Rules: 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 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' Types: A__U11 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> c:c1 tt :: tt:0':s:U11:U12:plus c :: c2:c3:c4 -> c:c1 A__U12 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> c2:c3:c4 c1 :: c:c1 c2 :: c5:c6:c7 -> c8:c9:c10:c11:c12:c13:c14 -> c2:c3:c4 A__PLUS :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> c5:c6:c7 mark :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus MARK :: tt:0':s:U11:U12:plus -> c8:c9:c10:c11:c12:c13:c14 c3 :: c5:c6:c7 -> c8:c9:c10:c11:c12:c13:c14 -> c2:c3:c4 c4 :: c2:c3:c4 0' :: tt:0':s:U11:U12:plus c5 :: c8:c9:c10:c11:c12:c13:c14 -> c5:c6:c7 s :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus c6 :: c:c1 -> c5:c6:c7 c7 :: c5:c6:c7 U11 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus c8 :: c:c1 -> c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 U12 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus c9 :: c2:c3:c4 -> c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 plus :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus c10 :: c5:c6:c7 -> c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 c11 :: c5:c6:c7 -> c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 c12 :: c8:c9:c10:c11:c12:c13:c14 c13 :: c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 c14 :: c8:c9:c10:c11:c12:c13:c14 a__U11 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus a__U12 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus a__plus :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus hole_c:c11_15 :: c:c1 hole_tt:0':s:U11:U12:plus2_15 :: tt:0':s:U11:U12:plus hole_c2:c3:c43_15 :: c2:c3:c4 hole_c5:c6:c74_15 :: c5:c6:c7 hole_c8:c9:c10:c11:c12:c13:c145_15 :: c8:c9:c10:c11:c12:c13:c14 gen_tt:0':s:U11:U12:plus6_15 :: Nat -> tt:0':s:U11:U12:plus gen_c8:c9:c10:c11:c12:c13:c147_15 :: Nat -> c8:c9:c10:c11:c12:c13:c14 Lemmas: mark(gen_tt:0':s:U11:U12:plus6_15(n27715_15)) -> gen_tt:0':s:U11:U12:plus6_15(n27715_15), rt in Omega(0) a__U11(gen_tt:0':s:U11:U12:plus6_15(0), gen_tt:0':s:U11:U12:plus6_15(n28840_15), gen_tt:0':s:U11:U12:plus6_15(c)) -> *8_15, rt in Omega(0) a__U12(gen_tt:0':s:U11:U12:plus6_15(0), gen_tt:0':s:U11:U12:plus6_15(n34579_15), gen_tt:0':s:U11:U12:plus6_15(c)) -> *8_15, rt in Omega(0) a__plus(gen_tt:0':s:U11:U12:plus6_15(a), gen_tt:0':s:U11:U12:plus6_15(+(1, n22156_15))) -> *8_15, rt in Omega(0) Generator Equations: gen_tt:0':s:U11:U12:plus6_15(0) <=> tt gen_tt:0':s:U11:U12:plus6_15(+(x, 1)) <=> s(gen_tt:0':s:U11:U12:plus6_15(x)) gen_c8:c9:c10:c11:c12:c13:c147_15(0) <=> c12 gen_c8:c9:c10:c11:c12:c13:c147_15(+(x, 1)) <=> c8(c(c2(c5(c12), c12)), gen_c8:c9:c10:c11:c12:c13:c147_15(x)) The following defined symbols remain to be analysed: A__U12, A__U11, A__PLUS, MARK They will be analysed ascendingly in the following order: A__U11 = A__U12 A__U11 = A__PLUS A__U11 = MARK A__U12 = A__PLUS A__U12 = MARK A__PLUS = MARK ---------------------------------------- (32) LowerBoundPropagationProof (FINISHED) Propagated lower bound. ---------------------------------------- (33) BOUNDS(n^1, INF) ---------------------------------------- (34) Obligation: Innermost TRS: Rules: 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 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' Types: A__U11 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> c:c1 tt :: tt:0':s:U11:U12:plus c :: c2:c3:c4 -> c:c1 A__U12 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> c2:c3:c4 c1 :: c:c1 c2 :: c5:c6:c7 -> c8:c9:c10:c11:c12:c13:c14 -> c2:c3:c4 A__PLUS :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> c5:c6:c7 mark :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus MARK :: tt:0':s:U11:U12:plus -> c8:c9:c10:c11:c12:c13:c14 c3 :: c5:c6:c7 -> c8:c9:c10:c11:c12:c13:c14 -> c2:c3:c4 c4 :: c2:c3:c4 0' :: tt:0':s:U11:U12:plus c5 :: c8:c9:c10:c11:c12:c13:c14 -> c5:c6:c7 s :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus c6 :: c:c1 -> c5:c6:c7 c7 :: c5:c6:c7 U11 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus c8 :: c:c1 -> c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 U12 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus c9 :: c2:c3:c4 -> c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 plus :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus c10 :: c5:c6:c7 -> c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 c11 :: c5:c6:c7 -> c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 c12 :: c8:c9:c10:c11:c12:c13:c14 c13 :: c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 c14 :: c8:c9:c10:c11:c12:c13:c14 a__U11 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus a__U12 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus a__plus :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus hole_c:c11_15 :: c:c1 hole_tt:0':s:U11:U12:plus2_15 :: tt:0':s:U11:U12:plus hole_c2:c3:c43_15 :: c2:c3:c4 hole_c5:c6:c74_15 :: c5:c6:c7 hole_c8:c9:c10:c11:c12:c13:c145_15 :: c8:c9:c10:c11:c12:c13:c14 gen_tt:0':s:U11:U12:plus6_15 :: Nat -> tt:0':s:U11:U12:plus gen_c8:c9:c10:c11:c12:c13:c147_15 :: Nat -> c8:c9:c10:c11:c12:c13:c14 Lemmas: mark(gen_tt:0':s:U11:U12:plus6_15(n27715_15)) -> gen_tt:0':s:U11:U12:plus6_15(n27715_15), rt in Omega(0) a__U11(gen_tt:0':s:U11:U12:plus6_15(0), gen_tt:0':s:U11:U12:plus6_15(n28840_15), gen_tt:0':s:U11:U12:plus6_15(c)) -> *8_15, rt in Omega(0) a__U12(gen_tt:0':s:U11:U12:plus6_15(0), gen_tt:0':s:U11:U12:plus6_15(n34579_15), gen_tt:0':s:U11:U12:plus6_15(c)) -> *8_15, rt in Omega(0) a__plus(gen_tt:0':s:U11:U12:plus6_15(a), gen_tt:0':s:U11:U12:plus6_15(+(1, n22156_15))) -> *8_15, rt in Omega(0) A__U12(gen_tt:0':s:U11:U12:plus6_15(0), gen_tt:0':s:U11:U12:plus6_15(n39961_15), gen_tt:0':s:U11:U12:plus6_15(c)) -> *8_15, rt in Omega(n39961_15) Generator Equations: gen_tt:0':s:U11:U12:plus6_15(0) <=> tt gen_tt:0':s:U11:U12:plus6_15(+(x, 1)) <=> s(gen_tt:0':s:U11:U12:plus6_15(x)) gen_c8:c9:c10:c11:c12:c13:c147_15(0) <=> c12 gen_c8:c9:c10:c11:c12:c13:c147_15(+(x, 1)) <=> c8(c(c2(c5(c12), c12)), gen_c8:c9:c10:c11:c12:c13:c147_15(x)) The following defined symbols remain to be analysed: A__PLUS, A__U11, MARK They will be analysed ascendingly in the following order: A__U11 = A__U12 A__U11 = A__PLUS A__U11 = MARK A__U12 = A__PLUS A__U12 = MARK A__PLUS = MARK ---------------------------------------- (35) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: A__PLUS(gen_tt:0':s:U11:U12:plus6_15(a), gen_tt:0':s:U11:U12:plus6_15(+(1, n50611_15))) -> *8_15, rt in Omega(n50611_15) Induction Base: A__PLUS(gen_tt:0':s:U11:U12:plus6_15(a), gen_tt:0':s:U11:U12:plus6_15(+(1, 0))) Induction Step: A__PLUS(gen_tt:0':s:U11:U12:plus6_15(a), gen_tt:0':s:U11:U12:plus6_15(+(1, +(n50611_15, 1)))) ->_R^Omega(1) c6(A__U11(tt, gen_tt:0':s:U11:U12:plus6_15(+(1, n50611_15)), gen_tt:0':s:U11:U12:plus6_15(a))) ->_R^Omega(1) c6(c(A__U12(tt, gen_tt:0':s:U11:U12:plus6_15(+(1, n50611_15)), gen_tt:0':s:U11:U12:plus6_15(a)))) ->_R^Omega(1) c6(c(c2(A__PLUS(mark(gen_tt:0':s:U11:U12:plus6_15(a)), mark(gen_tt:0':s:U11:U12:plus6_15(+(1, n50611_15)))), MARK(gen_tt:0':s:U11:U12:plus6_15(a))))) ->_L^Omega(0) c6(c(c2(A__PLUS(gen_tt:0':s:U11:U12:plus6_15(a), mark(gen_tt:0':s:U11:U12:plus6_15(+(1, n50611_15)))), MARK(gen_tt:0':s:U11:U12:plus6_15(a))))) ->_L^Omega(0) c6(c(c2(A__PLUS(gen_tt:0':s:U11:U12:plus6_15(a), gen_tt:0':s:U11:U12:plus6_15(+(1, n50611_15))), MARK(gen_tt:0':s:U11:U12:plus6_15(a))))) ->_IH c6(c(c2(*8_15, MARK(gen_tt:0':s:U11:U12:plus6_15(a))))) We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). ---------------------------------------- (36) Obligation: Innermost TRS: Rules: 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 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' Types: A__U11 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> c:c1 tt :: tt:0':s:U11:U12:plus c :: c2:c3:c4 -> c:c1 A__U12 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> c2:c3:c4 c1 :: c:c1 c2 :: c5:c6:c7 -> c8:c9:c10:c11:c12:c13:c14 -> c2:c3:c4 A__PLUS :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> c5:c6:c7 mark :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus MARK :: tt:0':s:U11:U12:plus -> c8:c9:c10:c11:c12:c13:c14 c3 :: c5:c6:c7 -> c8:c9:c10:c11:c12:c13:c14 -> c2:c3:c4 c4 :: c2:c3:c4 0' :: tt:0':s:U11:U12:plus c5 :: c8:c9:c10:c11:c12:c13:c14 -> c5:c6:c7 s :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus c6 :: c:c1 -> c5:c6:c7 c7 :: c5:c6:c7 U11 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus c8 :: c:c1 -> c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 U12 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus c9 :: c2:c3:c4 -> c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 plus :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus c10 :: c5:c6:c7 -> c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 c11 :: c5:c6:c7 -> c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 c12 :: c8:c9:c10:c11:c12:c13:c14 c13 :: c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 c14 :: c8:c9:c10:c11:c12:c13:c14 a__U11 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus a__U12 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus a__plus :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus hole_c:c11_15 :: c:c1 hole_tt:0':s:U11:U12:plus2_15 :: tt:0':s:U11:U12:plus hole_c2:c3:c43_15 :: c2:c3:c4 hole_c5:c6:c74_15 :: c5:c6:c7 hole_c8:c9:c10:c11:c12:c13:c145_15 :: c8:c9:c10:c11:c12:c13:c14 gen_tt:0':s:U11:U12:plus6_15 :: Nat -> tt:0':s:U11:U12:plus gen_c8:c9:c10:c11:c12:c13:c147_15 :: Nat -> c8:c9:c10:c11:c12:c13:c14 Lemmas: mark(gen_tt:0':s:U11:U12:plus6_15(n27715_15)) -> gen_tt:0':s:U11:U12:plus6_15(n27715_15), rt in Omega(0) a__U11(gen_tt:0':s:U11:U12:plus6_15(0), gen_tt:0':s:U11:U12:plus6_15(n28840_15), gen_tt:0':s:U11:U12:plus6_15(c)) -> *8_15, rt in Omega(0) a__U12(gen_tt:0':s:U11:U12:plus6_15(0), gen_tt:0':s:U11:U12:plus6_15(n34579_15), gen_tt:0':s:U11:U12:plus6_15(c)) -> *8_15, rt in Omega(0) a__plus(gen_tt:0':s:U11:U12:plus6_15(a), gen_tt:0':s:U11:U12:plus6_15(+(1, n22156_15))) -> *8_15, rt in Omega(0) A__U12(gen_tt:0':s:U11:U12:plus6_15(0), gen_tt:0':s:U11:U12:plus6_15(n39961_15), gen_tt:0':s:U11:U12:plus6_15(c)) -> *8_15, rt in Omega(n39961_15) A__PLUS(gen_tt:0':s:U11:U12:plus6_15(a), gen_tt:0':s:U11:U12:plus6_15(+(1, n50611_15))) -> *8_15, rt in Omega(n50611_15) Generator Equations: gen_tt:0':s:U11:U12:plus6_15(0) <=> tt gen_tt:0':s:U11:U12:plus6_15(+(x, 1)) <=> s(gen_tt:0':s:U11:U12:plus6_15(x)) gen_c8:c9:c10:c11:c12:c13:c147_15(0) <=> c12 gen_c8:c9:c10:c11:c12:c13:c147_15(+(x, 1)) <=> c8(c(c2(c5(c12), c12)), gen_c8:c9:c10:c11:c12:c13:c147_15(x)) The following defined symbols remain to be analysed: MARK, A__U11, A__U12 They will be analysed ascendingly in the following order: A__U11 = A__U12 A__U11 = A__PLUS A__U11 = MARK A__U12 = A__PLUS A__U12 = MARK A__PLUS = MARK ---------------------------------------- (37) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: MARK(gen_tt:0':s:U11:U12:plus6_15(+(1, n62106_15))) -> *8_15, rt in Omega(n62106_15) Induction Base: MARK(gen_tt:0':s:U11:U12:plus6_15(+(1, 0))) Induction Step: MARK(gen_tt:0':s:U11:U12:plus6_15(+(1, +(n62106_15, 1)))) ->_R^Omega(1) c13(MARK(gen_tt:0':s:U11:U12:plus6_15(+(1, n62106_15)))) ->_IH c13(*8_15) We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). ---------------------------------------- (38) Obligation: Innermost TRS: Rules: 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 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' Types: A__U11 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> c:c1 tt :: tt:0':s:U11:U12:plus c :: c2:c3:c4 -> c:c1 A__U12 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> c2:c3:c4 c1 :: c:c1 c2 :: c5:c6:c7 -> c8:c9:c10:c11:c12:c13:c14 -> c2:c3:c4 A__PLUS :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> c5:c6:c7 mark :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus MARK :: tt:0':s:U11:U12:plus -> c8:c9:c10:c11:c12:c13:c14 c3 :: c5:c6:c7 -> c8:c9:c10:c11:c12:c13:c14 -> c2:c3:c4 c4 :: c2:c3:c4 0' :: tt:0':s:U11:U12:plus c5 :: c8:c9:c10:c11:c12:c13:c14 -> c5:c6:c7 s :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus c6 :: c:c1 -> c5:c6:c7 c7 :: c5:c6:c7 U11 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus c8 :: c:c1 -> c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 U12 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus c9 :: c2:c3:c4 -> c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 plus :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus c10 :: c5:c6:c7 -> c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 c11 :: c5:c6:c7 -> c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 c12 :: c8:c9:c10:c11:c12:c13:c14 c13 :: c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 c14 :: c8:c9:c10:c11:c12:c13:c14 a__U11 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus a__U12 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus a__plus :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus hole_c:c11_15 :: c:c1 hole_tt:0':s:U11:U12:plus2_15 :: tt:0':s:U11:U12:plus hole_c2:c3:c43_15 :: c2:c3:c4 hole_c5:c6:c74_15 :: c5:c6:c7 hole_c8:c9:c10:c11:c12:c13:c145_15 :: c8:c9:c10:c11:c12:c13:c14 gen_tt:0':s:U11:U12:plus6_15 :: Nat -> tt:0':s:U11:U12:plus gen_c8:c9:c10:c11:c12:c13:c147_15 :: Nat -> c8:c9:c10:c11:c12:c13:c14 Lemmas: mark(gen_tt:0':s:U11:U12:plus6_15(n27715_15)) -> gen_tt:0':s:U11:U12:plus6_15(n27715_15), rt in Omega(0) a__U11(gen_tt:0':s:U11:U12:plus6_15(0), gen_tt:0':s:U11:U12:plus6_15(n28840_15), gen_tt:0':s:U11:U12:plus6_15(c)) -> *8_15, rt in Omega(0) a__U12(gen_tt:0':s:U11:U12:plus6_15(0), gen_tt:0':s:U11:U12:plus6_15(n34579_15), gen_tt:0':s:U11:U12:plus6_15(c)) -> *8_15, rt in Omega(0) a__plus(gen_tt:0':s:U11:U12:plus6_15(a), gen_tt:0':s:U11:U12:plus6_15(+(1, n22156_15))) -> *8_15, rt in Omega(0) A__U12(gen_tt:0':s:U11:U12:plus6_15(0), gen_tt:0':s:U11:U12:plus6_15(n39961_15), gen_tt:0':s:U11:U12:plus6_15(c)) -> *8_15, rt in Omega(n39961_15) A__PLUS(gen_tt:0':s:U11:U12:plus6_15(a), gen_tt:0':s:U11:U12:plus6_15(+(1, n50611_15))) -> *8_15, rt in Omega(n50611_15) MARK(gen_tt:0':s:U11:U12:plus6_15(+(1, n62106_15))) -> *8_15, rt in Omega(n62106_15) Generator Equations: gen_tt:0':s:U11:U12:plus6_15(0) <=> tt gen_tt:0':s:U11:U12:plus6_15(+(x, 1)) <=> s(gen_tt:0':s:U11:U12:plus6_15(x)) gen_c8:c9:c10:c11:c12:c13:c147_15(0) <=> c12 gen_c8:c9:c10:c11:c12:c13:c147_15(+(x, 1)) <=> c8(c(c2(c5(c12), c12)), gen_c8:c9:c10:c11:c12:c13:c147_15(x)) The following defined symbols remain to be analysed: A__U11, A__U12, A__PLUS They will be analysed ascendingly in the following order: A__U11 = A__U12 A__U11 = A__PLUS A__U11 = MARK A__U12 = A__PLUS A__U12 = MARK A__PLUS = MARK ---------------------------------------- (39) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: A__U11(gen_tt:0':s:U11:U12:plus6_15(0), gen_tt:0':s:U11:U12:plus6_15(n80965_15), gen_tt:0':s:U11:U12:plus6_15(c)) -> *8_15, rt in Omega(n80965_15) Induction Base: A__U11(gen_tt:0':s:U11:U12:plus6_15(0), gen_tt:0':s:U11:U12:plus6_15(0), gen_tt:0':s:U11:U12:plus6_15(c)) Induction Step: A__U11(gen_tt:0':s:U11:U12:plus6_15(0), gen_tt:0':s:U11:U12:plus6_15(+(n80965_15, 1)), gen_tt:0':s:U11:U12:plus6_15(c)) ->_R^Omega(1) c(A__U12(tt, gen_tt:0':s:U11:U12:plus6_15(+(n80965_15, 1)), gen_tt:0':s:U11:U12:plus6_15(c))) ->_R^Omega(1) c(c2(A__PLUS(mark(gen_tt:0':s:U11:U12:plus6_15(c)), mark(gen_tt:0':s:U11:U12:plus6_15(+(1, n80965_15)))), MARK(gen_tt:0':s:U11:U12:plus6_15(c)))) ->_L^Omega(0) c(c2(A__PLUS(gen_tt:0':s:U11:U12:plus6_15(c), mark(gen_tt:0':s:U11:U12:plus6_15(+(1, n80965_15)))), MARK(gen_tt:0':s:U11:U12:plus6_15(c)))) ->_L^Omega(0) c(c2(A__PLUS(gen_tt:0':s:U11:U12:plus6_15(c), gen_tt:0':s:U11:U12:plus6_15(+(1, n80965_15))), MARK(gen_tt:0':s:U11:U12:plus6_15(c)))) ->_R^Omega(1) c(c2(c6(A__U11(tt, gen_tt:0':s:U11:U12:plus6_15(n80965_15), gen_tt:0':s:U11:U12:plus6_15(c))), MARK(gen_tt:0':s:U11:U12:plus6_15(c)))) ->_IH c(c2(c6(*8_15), MARK(gen_tt:0':s:U11:U12:plus6_15(c)))) We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). ---------------------------------------- (40) Obligation: Innermost TRS: Rules: 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 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' Types: A__U11 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> c:c1 tt :: tt:0':s:U11:U12:plus c :: c2:c3:c4 -> c:c1 A__U12 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> c2:c3:c4 c1 :: c:c1 c2 :: c5:c6:c7 -> c8:c9:c10:c11:c12:c13:c14 -> c2:c3:c4 A__PLUS :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> c5:c6:c7 mark :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus MARK :: tt:0':s:U11:U12:plus -> c8:c9:c10:c11:c12:c13:c14 c3 :: c5:c6:c7 -> c8:c9:c10:c11:c12:c13:c14 -> c2:c3:c4 c4 :: c2:c3:c4 0' :: tt:0':s:U11:U12:plus c5 :: c8:c9:c10:c11:c12:c13:c14 -> c5:c6:c7 s :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus c6 :: c:c1 -> c5:c6:c7 c7 :: c5:c6:c7 U11 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus c8 :: c:c1 -> c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 U12 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus c9 :: c2:c3:c4 -> c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 plus :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus c10 :: c5:c6:c7 -> c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 c11 :: c5:c6:c7 -> c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 c12 :: c8:c9:c10:c11:c12:c13:c14 c13 :: c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 c14 :: c8:c9:c10:c11:c12:c13:c14 a__U11 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus a__U12 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus a__plus :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus hole_c:c11_15 :: c:c1 hole_tt:0':s:U11:U12:plus2_15 :: tt:0':s:U11:U12:plus hole_c2:c3:c43_15 :: c2:c3:c4 hole_c5:c6:c74_15 :: c5:c6:c7 hole_c8:c9:c10:c11:c12:c13:c145_15 :: c8:c9:c10:c11:c12:c13:c14 gen_tt:0':s:U11:U12:plus6_15 :: Nat -> tt:0':s:U11:U12:plus gen_c8:c9:c10:c11:c12:c13:c147_15 :: Nat -> c8:c9:c10:c11:c12:c13:c14 Lemmas: mark(gen_tt:0':s:U11:U12:plus6_15(n27715_15)) -> gen_tt:0':s:U11:U12:plus6_15(n27715_15), rt in Omega(0) a__U11(gen_tt:0':s:U11:U12:plus6_15(0), gen_tt:0':s:U11:U12:plus6_15(n28840_15), gen_tt:0':s:U11:U12:plus6_15(c)) -> *8_15, rt in Omega(0) a__U12(gen_tt:0':s:U11:U12:plus6_15(0), gen_tt:0':s:U11:U12:plus6_15(n34579_15), gen_tt:0':s:U11:U12:plus6_15(c)) -> *8_15, rt in Omega(0) a__plus(gen_tt:0':s:U11:U12:plus6_15(a), gen_tt:0':s:U11:U12:plus6_15(+(1, n22156_15))) -> *8_15, rt in Omega(0) A__U12(gen_tt:0':s:U11:U12:plus6_15(0), gen_tt:0':s:U11:U12:plus6_15(n39961_15), gen_tt:0':s:U11:U12:plus6_15(c)) -> *8_15, rt in Omega(n39961_15) A__PLUS(gen_tt:0':s:U11:U12:plus6_15(a), gen_tt:0':s:U11:U12:plus6_15(+(1, n50611_15))) -> *8_15, rt in Omega(n50611_15) MARK(gen_tt:0':s:U11:U12:plus6_15(+(1, n62106_15))) -> *8_15, rt in Omega(n62106_15) A__U11(gen_tt:0':s:U11:U12:plus6_15(0), gen_tt:0':s:U11:U12:plus6_15(n80965_15), gen_tt:0':s:U11:U12:plus6_15(c)) -> *8_15, rt in Omega(n80965_15) Generator Equations: gen_tt:0':s:U11:U12:plus6_15(0) <=> tt gen_tt:0':s:U11:U12:plus6_15(+(x, 1)) <=> s(gen_tt:0':s:U11:U12:plus6_15(x)) gen_c8:c9:c10:c11:c12:c13:c147_15(0) <=> c12 gen_c8:c9:c10:c11:c12:c13:c147_15(+(x, 1)) <=> c8(c(c2(c5(c12), c12)), gen_c8:c9:c10:c11:c12:c13:c147_15(x)) The following defined symbols remain to be analysed: A__U12, A__PLUS, MARK They will be analysed ascendingly in the following order: A__U11 = A__U12 A__U11 = A__PLUS A__U11 = MARK A__U12 = A__PLUS A__U12 = MARK A__PLUS = MARK ---------------------------------------- (41) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: A__U12(gen_tt:0':s:U11:U12:plus6_15(0), gen_tt:0':s:U11:U12:plus6_15(n93227_15), gen_tt:0':s:U11:U12:plus6_15(c)) -> *8_15, rt in Omega(n93227_15) Induction Base: A__U12(gen_tt:0':s:U11:U12:plus6_15(0), gen_tt:0':s:U11:U12:plus6_15(0), gen_tt:0':s:U11:U12:plus6_15(c)) Induction Step: A__U12(gen_tt:0':s:U11:U12:plus6_15(0), gen_tt:0':s:U11:U12:plus6_15(+(n93227_15, 1)), gen_tt:0':s:U11:U12:plus6_15(c)) ->_R^Omega(1) c2(A__PLUS(mark(gen_tt:0':s:U11:U12:plus6_15(c)), mark(gen_tt:0':s:U11:U12:plus6_15(+(n93227_15, 1)))), MARK(gen_tt:0':s:U11:U12:plus6_15(c))) ->_L^Omega(0) c2(A__PLUS(gen_tt:0':s:U11:U12:plus6_15(c), mark(gen_tt:0':s:U11:U12:plus6_15(+(1, n93227_15)))), MARK(gen_tt:0':s:U11:U12:plus6_15(c))) ->_L^Omega(0) c2(A__PLUS(gen_tt:0':s:U11:U12:plus6_15(c), gen_tt:0':s:U11:U12:plus6_15(+(1, n93227_15))), MARK(gen_tt:0':s:U11:U12:plus6_15(c))) ->_R^Omega(1) c2(c6(A__U11(tt, gen_tt:0':s:U11:U12:plus6_15(n93227_15), gen_tt:0':s:U11:U12:plus6_15(c))), MARK(gen_tt:0':s:U11:U12:plus6_15(c))) ->_R^Omega(1) c2(c6(c(A__U12(tt, gen_tt:0':s:U11:U12:plus6_15(n93227_15), gen_tt:0':s:U11:U12:plus6_15(c)))), MARK(gen_tt:0':s:U11:U12:plus6_15(c))) ->_IH c2(c6(c(*8_15)), MARK(gen_tt:0':s:U11:U12:plus6_15(c))) We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). ---------------------------------------- (42) Obligation: Innermost TRS: Rules: 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 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' Types: A__U11 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> c:c1 tt :: tt:0':s:U11:U12:plus c :: c2:c3:c4 -> c:c1 A__U12 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> c2:c3:c4 c1 :: c:c1 c2 :: c5:c6:c7 -> c8:c9:c10:c11:c12:c13:c14 -> c2:c3:c4 A__PLUS :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> c5:c6:c7 mark :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus MARK :: tt:0':s:U11:U12:plus -> c8:c9:c10:c11:c12:c13:c14 c3 :: c5:c6:c7 -> c8:c9:c10:c11:c12:c13:c14 -> c2:c3:c4 c4 :: c2:c3:c4 0' :: tt:0':s:U11:U12:plus c5 :: c8:c9:c10:c11:c12:c13:c14 -> c5:c6:c7 s :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus c6 :: c:c1 -> c5:c6:c7 c7 :: c5:c6:c7 U11 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus c8 :: c:c1 -> c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 U12 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus c9 :: c2:c3:c4 -> c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 plus :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus c10 :: c5:c6:c7 -> c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 c11 :: c5:c6:c7 -> c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 c12 :: c8:c9:c10:c11:c12:c13:c14 c13 :: c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 c14 :: c8:c9:c10:c11:c12:c13:c14 a__U11 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus a__U12 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus a__plus :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus hole_c:c11_15 :: c:c1 hole_tt:0':s:U11:U12:plus2_15 :: tt:0':s:U11:U12:plus hole_c2:c3:c43_15 :: c2:c3:c4 hole_c5:c6:c74_15 :: c5:c6:c7 hole_c8:c9:c10:c11:c12:c13:c145_15 :: c8:c9:c10:c11:c12:c13:c14 gen_tt:0':s:U11:U12:plus6_15 :: Nat -> tt:0':s:U11:U12:plus gen_c8:c9:c10:c11:c12:c13:c147_15 :: Nat -> c8:c9:c10:c11:c12:c13:c14 Lemmas: mark(gen_tt:0':s:U11:U12:plus6_15(n27715_15)) -> gen_tt:0':s:U11:U12:plus6_15(n27715_15), rt in Omega(0) a__U11(gen_tt:0':s:U11:U12:plus6_15(0), gen_tt:0':s:U11:U12:plus6_15(n28840_15), gen_tt:0':s:U11:U12:plus6_15(c)) -> *8_15, rt in Omega(0) a__U12(gen_tt:0':s:U11:U12:plus6_15(0), gen_tt:0':s:U11:U12:plus6_15(n34579_15), gen_tt:0':s:U11:U12:plus6_15(c)) -> *8_15, rt in Omega(0) a__plus(gen_tt:0':s:U11:U12:plus6_15(a), gen_tt:0':s:U11:U12:plus6_15(+(1, n22156_15))) -> *8_15, rt in Omega(0) A__U12(gen_tt:0':s:U11:U12:plus6_15(0), gen_tt:0':s:U11:U12:plus6_15(n93227_15), gen_tt:0':s:U11:U12:plus6_15(c)) -> *8_15, rt in Omega(n93227_15) A__PLUS(gen_tt:0':s:U11:U12:plus6_15(a), gen_tt:0':s:U11:U12:plus6_15(+(1, n50611_15))) -> *8_15, rt in Omega(n50611_15) MARK(gen_tt:0':s:U11:U12:plus6_15(+(1, n62106_15))) -> *8_15, rt in Omega(n62106_15) A__U11(gen_tt:0':s:U11:U12:plus6_15(0), gen_tt:0':s:U11:U12:plus6_15(n80965_15), gen_tt:0':s:U11:U12:plus6_15(c)) -> *8_15, rt in Omega(n80965_15) Generator Equations: gen_tt:0':s:U11:U12:plus6_15(0) <=> tt gen_tt:0':s:U11:U12:plus6_15(+(x, 1)) <=> s(gen_tt:0':s:U11:U12:plus6_15(x)) gen_c8:c9:c10:c11:c12:c13:c147_15(0) <=> c12 gen_c8:c9:c10:c11:c12:c13:c147_15(+(x, 1)) <=> c8(c(c2(c5(c12), c12)), gen_c8:c9:c10:c11:c12:c13:c147_15(x)) The following defined symbols remain to be analysed: A__PLUS, MARK They will be analysed ascendingly in the following order: A__U11 = A__U12 A__U11 = A__PLUS A__U11 = MARK A__U12 = A__PLUS A__U12 = MARK A__PLUS = MARK ---------------------------------------- (43) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: A__PLUS(gen_tt:0':s:U11:U12:plus6_15(a), gen_tt:0':s:U11:U12:plus6_15(+(1, n105734_15))) -> *8_15, rt in Omega(n105734_15) Induction Base: A__PLUS(gen_tt:0':s:U11:U12:plus6_15(a), gen_tt:0':s:U11:U12:plus6_15(+(1, 0))) Induction Step: A__PLUS(gen_tt:0':s:U11:U12:plus6_15(a), gen_tt:0':s:U11:U12:plus6_15(+(1, +(n105734_15, 1)))) ->_R^Omega(1) c6(A__U11(tt, gen_tt:0':s:U11:U12:plus6_15(+(1, n105734_15)), gen_tt:0':s:U11:U12:plus6_15(a))) ->_R^Omega(1) c6(c(A__U12(tt, gen_tt:0':s:U11:U12:plus6_15(+(1, n105734_15)), gen_tt:0':s:U11:U12:plus6_15(a)))) ->_R^Omega(1) c6(c(c2(A__PLUS(mark(gen_tt:0':s:U11:U12:plus6_15(a)), mark(gen_tt:0':s:U11:U12:plus6_15(+(1, n105734_15)))), MARK(gen_tt:0':s:U11:U12:plus6_15(a))))) ->_L^Omega(0) c6(c(c2(A__PLUS(gen_tt:0':s:U11:U12:plus6_15(a), mark(gen_tt:0':s:U11:U12:plus6_15(+(1, n105734_15)))), MARK(gen_tt:0':s:U11:U12:plus6_15(a))))) ->_L^Omega(0) c6(c(c2(A__PLUS(gen_tt:0':s:U11:U12:plus6_15(a), gen_tt:0':s:U11:U12:plus6_15(+(1, n105734_15))), MARK(gen_tt:0':s:U11:U12:plus6_15(a))))) ->_IH c6(c(c2(*8_15, MARK(gen_tt:0':s:U11:U12:plus6_15(a))))) We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). ---------------------------------------- (44) Obligation: Innermost TRS: Rules: 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 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' Types: A__U11 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> c:c1 tt :: tt:0':s:U11:U12:plus c :: c2:c3:c4 -> c:c1 A__U12 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> c2:c3:c4 c1 :: c:c1 c2 :: c5:c6:c7 -> c8:c9:c10:c11:c12:c13:c14 -> c2:c3:c4 A__PLUS :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> c5:c6:c7 mark :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus MARK :: tt:0':s:U11:U12:plus -> c8:c9:c10:c11:c12:c13:c14 c3 :: c5:c6:c7 -> c8:c9:c10:c11:c12:c13:c14 -> c2:c3:c4 c4 :: c2:c3:c4 0' :: tt:0':s:U11:U12:plus c5 :: c8:c9:c10:c11:c12:c13:c14 -> c5:c6:c7 s :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus c6 :: c:c1 -> c5:c6:c7 c7 :: c5:c6:c7 U11 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus c8 :: c:c1 -> c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 U12 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus c9 :: c2:c3:c4 -> c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 plus :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus c10 :: c5:c6:c7 -> c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 c11 :: c5:c6:c7 -> c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 c12 :: c8:c9:c10:c11:c12:c13:c14 c13 :: c8:c9:c10:c11:c12:c13:c14 -> c8:c9:c10:c11:c12:c13:c14 c14 :: c8:c9:c10:c11:c12:c13:c14 a__U11 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus a__U12 :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus a__plus :: tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus -> tt:0':s:U11:U12:plus hole_c:c11_15 :: c:c1 hole_tt:0':s:U11:U12:plus2_15 :: tt:0':s:U11:U12:plus hole_c2:c3:c43_15 :: c2:c3:c4 hole_c5:c6:c74_15 :: c5:c6:c7 hole_c8:c9:c10:c11:c12:c13:c145_15 :: c8:c9:c10:c11:c12:c13:c14 gen_tt:0':s:U11:U12:plus6_15 :: Nat -> tt:0':s:U11:U12:plus gen_c8:c9:c10:c11:c12:c13:c147_15 :: Nat -> c8:c9:c10:c11:c12:c13:c14 Lemmas: mark(gen_tt:0':s:U11:U12:plus6_15(n27715_15)) -> gen_tt:0':s:U11:U12:plus6_15(n27715_15), rt in Omega(0) a__U11(gen_tt:0':s:U11:U12:plus6_15(0), gen_tt:0':s:U11:U12:plus6_15(n28840_15), gen_tt:0':s:U11:U12:plus6_15(c)) -> *8_15, rt in Omega(0) a__U12(gen_tt:0':s:U11:U12:plus6_15(0), gen_tt:0':s:U11:U12:plus6_15(n34579_15), gen_tt:0':s:U11:U12:plus6_15(c)) -> *8_15, rt in Omega(0) a__plus(gen_tt:0':s:U11:U12:plus6_15(a), gen_tt:0':s:U11:U12:plus6_15(+(1, n22156_15))) -> *8_15, rt in Omega(0) A__U12(gen_tt:0':s:U11:U12:plus6_15(0), gen_tt:0':s:U11:U12:plus6_15(n93227_15), gen_tt:0':s:U11:U12:plus6_15(c)) -> *8_15, rt in Omega(n93227_15) A__PLUS(gen_tt:0':s:U11:U12:plus6_15(a), gen_tt:0':s:U11:U12:plus6_15(+(1, n105734_15))) -> *8_15, rt in Omega(n105734_15) MARK(gen_tt:0':s:U11:U12:plus6_15(+(1, n62106_15))) -> *8_15, rt in Omega(n62106_15) A__U11(gen_tt:0':s:U11:U12:plus6_15(0), gen_tt:0':s:U11:U12:plus6_15(n80965_15), gen_tt:0':s:U11:U12:plus6_15(c)) -> *8_15, rt in Omega(n80965_15) Generator Equations: gen_tt:0':s:U11:U12:plus6_15(0) <=> tt gen_tt:0':s:U11:U12:plus6_15(+(x, 1)) <=> s(gen_tt:0':s:U11:U12:plus6_15(x)) gen_c8:c9:c10:c11:c12:c13:c147_15(0) <=> c12 gen_c8:c9:c10:c11:c12:c13:c147_15(+(x, 1)) <=> c8(c(c2(c5(c12), c12)), gen_c8:c9:c10:c11:c12:c13:c147_15(x)) The following defined symbols remain to be analysed: MARK They will be analysed ascendingly in the following order: A__U11 = A__U12 A__U11 = A__PLUS A__U11 = MARK A__U12 = A__PLUS A__U12 = MARK A__PLUS = MARK ---------------------------------------- (45) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: MARK(gen_tt:0':s:U11:U12:plus6_15(+(1, n118612_15))) -> *8_15, rt in Omega(n118612_15) Induction Base: MARK(gen_tt:0':s:U11:U12:plus6_15(+(1, 0))) Induction Step: MARK(gen_tt:0':s:U11:U12:plus6_15(+(1, +(n118612_15, 1)))) ->_R^Omega(1) c13(MARK(gen_tt:0':s:U11:U12:plus6_15(+(1, n118612_15)))) ->_IH c13(*8_15) We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). ---------------------------------------- (46) BOUNDS(1, INF) ---------------------------------------- (47) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT ---------------------------------------- (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__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 ---------------------------------------- (49) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing nodes: MARK(0) -> c14 A__U12(z0, z1, z2) -> c4 MARK(tt) -> c12 A__PLUS(z0, z1) -> c7 A__U11(z0, z1, z2) -> c1 ---------------------------------------- (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__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 ---------------------------------------- (51) CdtToCpxRelTrsProof (BOTH BOUNDS(ID, ID)) Converted S to standard rules, and D \ S as well as R to relative rules. ---------------------------------------- (52) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: A__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)) The (relative) TRS S consists of the following 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 Rewrite Strategy: INNERMOST ---------------------------------------- (53) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (54) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: A__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)) 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 S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (55) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (56) 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, z0, z1) -> c(A__U12(tt, z0, z1)) [1] A__U12(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1)) [1] A__U12(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0)) [1] A__PLUS(z0, 0) -> c5(MARK(z0)) [1] A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) [1] MARK(U11(z0, z1, z2)) -> c8(A__U11(mark(z0), z1, z2), MARK(z0)) [1] MARK(U12(z0, z1, z2)) -> c9(A__U12(mark(z0), z1, z2), MARK(z0)) [1] MARK(plus(z0, z1)) -> c10(A__PLUS(mark(z0), mark(z1)), MARK(z0)) [1] MARK(plus(z0, z1)) -> c11(A__PLUS(mark(z0), mark(z1)), MARK(z1)) [1] MARK(s(z0)) -> c13(MARK(z0)) [1] a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) [0] a__U11(z0, z1, z2) -> U11(z0, z1, z2) [0] a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) [0] a__U12(z0, z1, z2) -> U12(z0, z1, z2) [0] a__plus(z0, 0) -> mark(z0) [0] a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) [0] a__plus(z0, z1) -> plus(z0, z1) [0] mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) [0] mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) [0] mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) [0] mark(tt) -> tt [0] mark(s(z0)) -> s(mark(z0)) [0] mark(0) -> 0 [0] Rewrite Strategy: INNERMOST ---------------------------------------- (57) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (58) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) [1] A__U12(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1)) [1] A__U12(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0)) [1] A__PLUS(z0, 0) -> c5(MARK(z0)) [1] A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) [1] MARK(U11(z0, z1, z2)) -> c8(A__U11(mark(z0), z1, z2), MARK(z0)) [1] MARK(U12(z0, z1, z2)) -> c9(A__U12(mark(z0), z1, z2), MARK(z0)) [1] MARK(plus(z0, z1)) -> c10(A__PLUS(mark(z0), mark(z1)), MARK(z0)) [1] MARK(plus(z0, z1)) -> c11(A__PLUS(mark(z0), mark(z1)), MARK(z1)) [1] MARK(s(z0)) -> c13(MARK(z0)) [1] a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) [0] a__U11(z0, z1, z2) -> U11(z0, z1, z2) [0] a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) [0] a__U12(z0, z1, z2) -> U12(z0, z1, z2) [0] a__plus(z0, 0) -> mark(z0) [0] a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) [0] a__plus(z0, z1) -> plus(z0, z1) [0] mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) [0] mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) [0] mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) [0] mark(tt) -> tt [0] mark(s(z0)) -> s(mark(z0)) [0] mark(0) -> 0 [0] The TRS has the following type information: A__U11 :: tt:0:s:U11:U12:plus -> tt:0:s:U11:U12:plus -> tt:0:s:U11:U12:plus -> c tt :: tt:0:s:U11:U12:plus c :: c2:c3 -> c A__U12 :: tt:0:s:U11:U12:plus -> tt:0:s:U11:U12:plus -> tt:0:s:U11:U12:plus -> c2:c3 c2 :: c5:c6 -> c8:c9:c10:c11:c13 -> c2:c3 A__PLUS :: tt:0:s:U11:U12:plus -> tt:0:s:U11:U12:plus -> c5:c6 mark :: tt:0:s:U11:U12:plus -> tt:0:s:U11:U12:plus MARK :: tt:0:s:U11:U12:plus -> c8:c9:c10:c11:c13 c3 :: c5:c6 -> c8:c9:c10:c11:c13 -> c2:c3 0 :: tt:0:s:U11:U12:plus c5 :: c8:c9:c10:c11:c13 -> c5:c6 s :: tt:0:s:U11:U12:plus -> tt:0:s:U11:U12:plus c6 :: c -> c5:c6 U11 :: tt:0:s:U11:U12:plus -> tt:0:s:U11:U12:plus -> tt:0:s:U11:U12:plus -> tt:0:s:U11:U12:plus c8 :: c -> c8:c9:c10:c11:c13 -> c8:c9:c10:c11:c13 U12 :: tt:0:s:U11:U12:plus -> tt:0:s:U11:U12:plus -> tt:0:s:U11:U12:plus -> tt:0:s:U11:U12:plus c9 :: c2:c3 -> c8:c9:c10:c11:c13 -> c8:c9:c10:c11:c13 plus :: tt:0:s:U11:U12:plus -> tt:0:s:U11:U12:plus -> tt:0:s:U11:U12:plus c10 :: c5:c6 -> c8:c9:c10:c11:c13 -> c8:c9:c10:c11:c13 c11 :: c5:c6 -> c8:c9:c10:c11:c13 -> c8:c9:c10:c11:c13 c13 :: c8:c9:c10:c11:c13 -> c8:c9:c10:c11:c13 a__U11 :: tt:0:s:U11:U12:plus -> tt:0:s:U11:U12:plus -> tt:0:s:U11:U12:plus -> tt:0:s:U11:U12:plus a__U12 :: tt:0:s:U11:U12:plus -> tt:0:s:U11:U12:plus -> tt:0:s:U11:U12:plus -> tt:0:s:U11:U12:plus a__plus :: tt:0:s:U11:U12:plus -> tt:0:s:U11:U12:plus -> tt:0:s:U11:U12:plus Rewrite Strategy: INNERMOST ---------------------------------------- (59) CompletionProof (UPPER BOUND(ID)) The transformation into a RNTS is sound, since: (a) The obligation is a constructor system where every type has a constant constructor, (b) The following defined symbols do not have to be completely defined, as they can never occur inside other defined symbols: A__U11_3 A__U12_3 A__PLUS_2 MARK_1 (c) The following functions are completely defined: a__U11_3 a__U12_3 a__plus_2 mark_1 Due to the following rules being added: a__U11(v0, v1, v2) -> null_a__U11 [0] a__U12(v0, v1, v2) -> null_a__U12 [0] a__plus(v0, v1) -> null_a__plus [0] mark(v0) -> null_mark [0] And the following fresh constants: null_a__U11, null_a__U12, null_a__plus, null_mark, const, const1, const2, const3 ---------------------------------------- (60) 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, z0, z1) -> c(A__U12(tt, z0, z1)) [1] A__U12(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1)) [1] A__U12(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0)) [1] A__PLUS(z0, 0) -> c5(MARK(z0)) [1] A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) [1] MARK(U11(z0, z1, z2)) -> c8(A__U11(mark(z0), z1, z2), MARK(z0)) [1] MARK(U12(z0, z1, z2)) -> c9(A__U12(mark(z0), z1, z2), MARK(z0)) [1] MARK(plus(z0, z1)) -> c10(A__PLUS(mark(z0), mark(z1)), MARK(z0)) [1] MARK(plus(z0, z1)) -> c11(A__PLUS(mark(z0), mark(z1)), MARK(z1)) [1] MARK(s(z0)) -> c13(MARK(z0)) [1] a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) [0] a__U11(z0, z1, z2) -> U11(z0, z1, z2) [0] a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) [0] a__U12(z0, z1, z2) -> U12(z0, z1, z2) [0] a__plus(z0, 0) -> mark(z0) [0] a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) [0] a__plus(z0, z1) -> plus(z0, z1) [0] mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) [0] mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) [0] mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) [0] mark(tt) -> tt [0] mark(s(z0)) -> s(mark(z0)) [0] mark(0) -> 0 [0] a__U11(v0, v1, v2) -> null_a__U11 [0] a__U12(v0, v1, v2) -> null_a__U12 [0] a__plus(v0, v1) -> null_a__plus [0] mark(v0) -> null_mark [0] The TRS has the following type information: A__U11 :: tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> c tt :: tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark c :: c2:c3 -> c A__U12 :: tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> c2:c3 c2 :: c5:c6 -> c8:c9:c10:c11:c13 -> c2:c3 A__PLUS :: tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> c5:c6 mark :: tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark MARK :: tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> c8:c9:c10:c11:c13 c3 :: c5:c6 -> c8:c9:c10:c11:c13 -> c2:c3 0 :: tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark c5 :: c8:c9:c10:c11:c13 -> c5:c6 s :: tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark c6 :: c -> c5:c6 U11 :: tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark c8 :: c -> c8:c9:c10:c11:c13 -> c8:c9:c10:c11:c13 U12 :: tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark c9 :: c2:c3 -> c8:c9:c10:c11:c13 -> c8:c9:c10:c11:c13 plus :: tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark c10 :: c5:c6 -> c8:c9:c10:c11:c13 -> c8:c9:c10:c11:c13 c11 :: c5:c6 -> c8:c9:c10:c11:c13 -> c8:c9:c10:c11:c13 c13 :: c8:c9:c10:c11:c13 -> c8:c9:c10:c11:c13 a__U11 :: tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark a__U12 :: tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark a__plus :: tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark null_a__U11 :: tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark null_a__U12 :: tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark null_a__plus :: tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark null_mark :: tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark const :: c const1 :: c2:c3 const2 :: c5:c6 const3 :: c8:c9:c10:c11:c13 Rewrite Strategy: INNERMOST ---------------------------------------- (61) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (62) 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, z0, z1) -> c(A__U12(tt, z0, z1)) [1] A__U12(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1)) [1] A__U12(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0)) [1] A__PLUS(z0, 0) -> c5(MARK(z0)) [1] A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) [1] MARK(U11(U11(z063, z147, z231), z1, z2)) -> c8(A__U11(a__U11(mark(z063), z147, z231), z1, z2), MARK(U11(z063, z147, z231))) [1] MARK(U11(U12(z064, z148, z232), z1, z2)) -> c8(A__U11(a__U12(mark(z064), z148, z232), z1, z2), MARK(U12(z064, z148, z232))) [1] MARK(U11(plus(z065, z149), z1, z2)) -> c8(A__U11(a__plus(mark(z065), mark(z149)), z1, z2), MARK(plus(z065, z149))) [1] MARK(U11(tt, z1, z2)) -> c8(A__U11(tt, z1, z2), MARK(tt)) [1] MARK(U11(s(z066), z1, z2)) -> c8(A__U11(s(mark(z066)), z1, z2), MARK(s(z066))) [1] MARK(U11(0, z1, z2)) -> c8(A__U11(0, z1, z2), MARK(0)) [1] MARK(U11(z0, z1, z2)) -> c8(A__U11(null_mark, z1, z2), MARK(z0)) [1] MARK(U12(U11(z067, z150, z233), z1, z2)) -> c9(A__U12(a__U11(mark(z067), z150, z233), z1, z2), MARK(U11(z067, z150, z233))) [1] MARK(U12(U12(z068, z151, z234), z1, z2)) -> c9(A__U12(a__U12(mark(z068), z151, z234), z1, z2), MARK(U12(z068, z151, z234))) [1] MARK(U12(plus(z069, z152), z1, z2)) -> c9(A__U12(a__plus(mark(z069), mark(z152)), z1, z2), MARK(plus(z069, z152))) [1] MARK(U12(tt, z1, z2)) -> c9(A__U12(tt, z1, z2), MARK(tt)) [1] MARK(U12(s(z070), z1, z2)) -> c9(A__U12(s(mark(z070)), z1, z2), MARK(s(z070))) [1] MARK(U12(0, z1, z2)) -> c9(A__U12(0, z1, z2), MARK(0)) [1] MARK(U12(z0, z1, z2)) -> c9(A__U12(null_mark, z1, z2), MARK(z0)) [1] MARK(plus(z0, z1)) -> c10(A__PLUS(mark(z0), mark(z1)), MARK(z0)) [1] MARK(plus(z0, z1)) -> c11(A__PLUS(mark(z0), mark(z1)), MARK(z1)) [1] MARK(s(z0)) -> c13(MARK(z0)) [1] a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) [0] a__U11(z0, z1, z2) -> U11(z0, z1, z2) [0] a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) [0] a__U12(z0, z1, z2) -> U12(z0, z1, z2) [0] a__plus(z0, 0) -> mark(z0) [0] a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) [0] a__plus(z0, z1) -> plus(z0, z1) [0] mark(U11(U11(z0167, z1125, z283), z1, z2)) -> a__U11(a__U11(mark(z0167), z1125, z283), z1, z2) [0] mark(U11(U12(z0168, z1126, z284), z1, z2)) -> a__U11(a__U12(mark(z0168), z1126, z284), z1, z2) [0] mark(U11(plus(z0169, z1127), z1, z2)) -> a__U11(a__plus(mark(z0169), mark(z1127)), z1, z2) [0] mark(U11(tt, z1, z2)) -> a__U11(tt, z1, z2) [0] mark(U11(s(z0170), z1, z2)) -> a__U11(s(mark(z0170)), z1, z2) [0] mark(U11(0, z1, z2)) -> a__U11(0, z1, z2) [0] mark(U11(z0, z1, z2)) -> a__U11(null_mark, z1, z2) [0] mark(U12(U11(z0171, z1128, z285), z1, z2)) -> a__U12(a__U11(mark(z0171), z1128, z285), z1, z2) [0] mark(U12(U12(z0172, z1129, z286), z1, z2)) -> a__U12(a__U12(mark(z0172), z1129, z286), z1, z2) [0] mark(U12(plus(z0173, z1130), z1, z2)) -> a__U12(a__plus(mark(z0173), mark(z1130)), z1, z2) [0] mark(U12(tt, z1, z2)) -> a__U12(tt, z1, z2) [0] mark(U12(s(z0174), z1, z2)) -> a__U12(s(mark(z0174)), z1, z2) [0] mark(U12(0, z1, z2)) -> a__U12(0, z1, z2) [0] mark(U12(z0, z1, z2)) -> a__U12(null_mark, z1, z2) [0] mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) [0] mark(tt) -> tt [0] mark(s(z0)) -> s(mark(z0)) [0] mark(0) -> 0 [0] a__U11(v0, v1, v2) -> null_a__U11 [0] a__U12(v0, v1, v2) -> null_a__U12 [0] a__plus(v0, v1) -> null_a__plus [0] mark(v0) -> null_mark [0] The TRS has the following type information: A__U11 :: tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> c tt :: tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark c :: c2:c3 -> c A__U12 :: tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> c2:c3 c2 :: c5:c6 -> c8:c9:c10:c11:c13 -> c2:c3 A__PLUS :: tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> c5:c6 mark :: tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark MARK :: tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> c8:c9:c10:c11:c13 c3 :: c5:c6 -> c8:c9:c10:c11:c13 -> c2:c3 0 :: tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark c5 :: c8:c9:c10:c11:c13 -> c5:c6 s :: tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark c6 :: c -> c5:c6 U11 :: tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark c8 :: c -> c8:c9:c10:c11:c13 -> c8:c9:c10:c11:c13 U12 :: tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark c9 :: c2:c3 -> c8:c9:c10:c11:c13 -> c8:c9:c10:c11:c13 plus :: tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark c10 :: c5:c6 -> c8:c9:c10:c11:c13 -> c8:c9:c10:c11:c13 c11 :: c5:c6 -> c8:c9:c10:c11:c13 -> c8:c9:c10:c11:c13 c13 :: c8:c9:c10:c11:c13 -> c8:c9:c10:c11:c13 a__U11 :: tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark a__U12 :: tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark a__plus :: tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark null_a__U11 :: tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark null_a__U12 :: tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark null_a__plus :: tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark null_mark :: tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark const :: c const1 :: c2:c3 const2 :: c5:c6 const3 :: c8:c9:c10:c11:c13 Rewrite Strategy: INNERMOST ---------------------------------------- (63) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: tt => 1 0 => 0 null_a__U11 => 0 null_a__U12 => 0 null_a__plus => 0 null_mark => 0 const => 0 const1 => 0 const2 => 0 const3 => 0 ---------------------------------------- (64) Obligation: Complexity RNTS consisting of the following rules: A__PLUS(z, z') -{ 1 }-> 1 + MARK(z0) :|: z = z0, z0 >= 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U11(1, z1, z0) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1 A__U11(z, z', z'') -{ 1 }-> 1 + A__U12(1, z0, z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 A__U12(z, z', z'') -{ 1 }-> 1 + A__PLUS(mark(z1), mark(z0)) + MARK(z0) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 A__U12(z, z', z'') -{ 1 }-> 1 + A__PLUS(mark(z1), mark(z0)) + MARK(z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(a__plus(mark(z069), mark(z152)), z1, z2) + MARK(1 + z069 + z152) :|: z1 >= 0, z = 1 + (1 + z069 + z152) + z1 + z2, z152 >= 0, z069 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(a__U12(mark(z068), z151, z234), z1, z2) + MARK(1 + z068 + z151 + z234) :|: z = 1 + (1 + z068 + z151 + z234) + z1 + z2, z151 >= 0, z1 >= 0, z068 >= 0, z234 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(a__U11(mark(z067), z150, z233), z1, z2) + MARK(1 + z067 + z150 + z233) :|: z1 >= 0, z233 >= 0, z = 1 + (1 + z067 + z150 + z233) + z1 + z2, z150 >= 0, z2 >= 0, z067 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(1, z1, z2) + MARK(1) :|: z1 >= 0, z = 1 + 1 + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(0, z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(0, z1, z2) + MARK(0) :|: z1 >= 0, z = 1 + 0 + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(1 + mark(z070), z1, z2) + MARK(1 + z070) :|: z1 >= 0, z = 1 + (1 + z070) + z1 + z2, z070 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(a__plus(mark(z065), mark(z149)), z1, z2) + MARK(1 + z065 + z149) :|: z = 1 + (1 + z065 + z149) + z1 + z2, z149 >= 0, z1 >= 0, z065 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(a__U12(mark(z064), z148, z232), z1, z2) + MARK(1 + z064 + z148 + z232) :|: z1 >= 0, z148 >= 0, z064 >= 0, z232 >= 0, z2 >= 0, z = 1 + (1 + z064 + z148 + z232) + z1 + z2 MARK(z) -{ 1 }-> 1 + A__U11(a__U11(mark(z063), z147, z231), z1, z2) + MARK(1 + z063 + z147 + z231) :|: z063 >= 0, z1 >= 0, z231 >= 0, z147 >= 0, z = 1 + (1 + z063 + z147 + z231) + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(1, z1, z2) + MARK(1) :|: z1 >= 0, z = 1 + 1 + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(0, z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(0, z1, z2) + MARK(0) :|: z1 >= 0, z = 1 + 0 + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(1 + mark(z066), z1, z2) + MARK(1 + z066) :|: z1 >= 0, z = 1 + (1 + z066) + z1 + z2, z066 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__PLUS(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__PLUS(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__U11(z, z', z'') -{ 0 }-> a__U12(1, z0, z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 a__U11(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 a__U11(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 a__U12(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 a__U12(z, z', z'') -{ 0 }-> 1 + a__plus(mark(z1), mark(z0)) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 a__U12(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 a__plus(z, z') -{ 0 }-> mark(z0) :|: z = z0, z0 >= 0, z' = 0 a__plus(z, z') -{ 0 }-> a__U11(1, z1, z0) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1 a__plus(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__plus(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 mark(z) -{ 0 }-> a__plus(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U12(a__plus(mark(z0173), mark(z1130)), z1, z2) :|: z1130 >= 0, z1 >= 0, z0173 >= 0, z = 1 + (1 + z0173 + z1130) + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__U12(a__U12(mark(z0172), z1129, z286), z1, z2) :|: z286 >= 0, z1 >= 0, z = 1 + (1 + z0172 + z1129 + z286) + z1 + z2, z0172 >= 0, z1129 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U12(a__U11(mark(z0171), z1128, z285), z1, z2) :|: z1 >= 0, z0171 >= 0, z = 1 + (1 + z0171 + z1128 + z285) + z1 + z2, z1128 >= 0, z2 >= 0, z285 >= 0 mark(z) -{ 0 }-> a__U12(1, z1, z2) :|: z1 >= 0, z = 1 + 1 + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__U12(0, z1, z2) :|: z1 >= 0, z = 1 + 0 + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__U12(0, z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U12(1 + mark(z0174), z1, z2) :|: z0174 >= 0, z1 >= 0, z = 1 + (1 + z0174) + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__U11(a__plus(mark(z0169), mark(z1127)), z1, z2) :|: z1127 >= 0, z1 >= 0, z = 1 + (1 + z0169 + z1127) + z1 + z2, z0169 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U11(a__U12(mark(z0168), z1126, z284), z1, z2) :|: z0168 >= 0, z1 >= 0, z = 1 + (1 + z0168 + z1126 + z284) + z1 + z2, z284 >= 0, z1126 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U11(a__U11(mark(z0167), z1125, z283), z1, z2) :|: z0167 >= 0, z1 >= 0, z = 1 + (1 + z0167 + z1125 + z283) + z1 + z2, z1125 >= 0, z283 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U11(1, z1, z2) :|: z1 >= 0, z = 1 + 1 + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__U11(0, z1, z2) :|: z1 >= 0, z = 1 + 0 + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__U11(0, z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U11(1 + mark(z0170), z1, z2) :|: z0170 >= 0, z1 >= 0, z = 1 + (1 + z0170) + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> 1 :|: z = 1 mark(z) -{ 0 }-> 0 :|: z = 0 mark(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 mark(z) -{ 0 }-> 1 + mark(z0) :|: z = 1 + z0, z0 >= 0 ---------------------------------------- (65) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (66) Obligation: Complexity RNTS consisting of the following rules: A__PLUS(z, z') -{ 1 }-> 1 + MARK(z) :|: z >= 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U11(1, z' - 1, z) :|: z' - 1 >= 0, z >= 0 A__U11(z, z', z'') -{ 1 }-> 1 + A__U12(1, z', z'') :|: z'' >= 0, z = 1, z' >= 0 A__U12(z, z', z'') -{ 1 }-> 1 + A__PLUS(mark(z''), mark(z')) + MARK(z') :|: z'' >= 0, z = 1, z' >= 0 A__U12(z, z', z'') -{ 1 }-> 1 + A__PLUS(mark(z''), mark(z')) + MARK(z'') :|: z'' >= 0, z = 1, z' >= 0 MARK(z) -{ 1 }-> 1 + MARK(z - 1) :|: z - 1 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(a__plus(mark(z069), mark(z152)), z1, z2) + MARK(1 + z069 + z152) :|: z1 >= 0, z = 1 + (1 + z069 + z152) + z1 + z2, z152 >= 0, z069 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(a__U12(mark(z068), z151, z234), z1, z2) + MARK(1 + z068 + z151 + z234) :|: z = 1 + (1 + z068 + z151 + z234) + z1 + z2, z151 >= 0, z1 >= 0, z068 >= 0, z234 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(a__U11(mark(z067), z150, z233), z1, z2) + MARK(1 + z067 + z150 + z233) :|: z1 >= 0, z233 >= 0, z = 1 + (1 + z067 + z150 + z233) + z1 + z2, z150 >= 0, z2 >= 0, z067 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(1, z1, z2) + MARK(1) :|: z1 >= 0, z = 1 + 1 + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(0, z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(0, z1, z2) + MARK(0) :|: z1 >= 0, z = 1 + 0 + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(1 + mark(z070), z1, z2) + MARK(1 + z070) :|: z1 >= 0, z = 1 + (1 + z070) + z1 + z2, z070 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(a__plus(mark(z065), mark(z149)), z1, z2) + MARK(1 + z065 + z149) :|: z = 1 + (1 + z065 + z149) + z1 + z2, z149 >= 0, z1 >= 0, z065 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(a__U12(mark(z064), z148, z232), z1, z2) + MARK(1 + z064 + z148 + z232) :|: z1 >= 0, z148 >= 0, z064 >= 0, z232 >= 0, z2 >= 0, z = 1 + (1 + z064 + z148 + z232) + z1 + z2 MARK(z) -{ 1 }-> 1 + A__U11(a__U11(mark(z063), z147, z231), z1, z2) + MARK(1 + z063 + z147 + z231) :|: z063 >= 0, z1 >= 0, z231 >= 0, z147 >= 0, z = 1 + (1 + z063 + z147 + z231) + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(1, z1, z2) + MARK(1) :|: z1 >= 0, z = 1 + 1 + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(0, z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(0, z1, z2) + MARK(0) :|: z1 >= 0, z = 1 + 0 + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(1 + mark(z066), z1, z2) + MARK(1 + z066) :|: z1 >= 0, z = 1 + (1 + z066) + z1 + z2, z066 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__PLUS(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__PLUS(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__U11(z, z', z'') -{ 0 }-> a__U12(1, z', z'') :|: z'' >= 0, z = 1, z' >= 0 a__U11(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 a__U11(z, z', z'') -{ 0 }-> 1 + z + z' + z'' :|: z' >= 0, z >= 0, z'' >= 0 a__U12(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 a__U12(z, z', z'') -{ 0 }-> 1 + a__plus(mark(z''), mark(z')) :|: z'' >= 0, z = 1, z' >= 0 a__U12(z, z', z'') -{ 0 }-> 1 + z + z' + z'' :|: z' >= 0, z >= 0, z'' >= 0 a__plus(z, z') -{ 0 }-> mark(z) :|: z >= 0, z' = 0 a__plus(z, z') -{ 0 }-> a__U11(1, z' - 1, z) :|: z' - 1 >= 0, z >= 0 a__plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 a__plus(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 mark(z) -{ 0 }-> a__plus(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U12(a__plus(mark(z0173), mark(z1130)), z1, z2) :|: z1130 >= 0, z1 >= 0, z0173 >= 0, z = 1 + (1 + z0173 + z1130) + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__U12(a__U12(mark(z0172), z1129, z286), z1, z2) :|: z286 >= 0, z1 >= 0, z = 1 + (1 + z0172 + z1129 + z286) + z1 + z2, z0172 >= 0, z1129 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U12(a__U11(mark(z0171), z1128, z285), z1, z2) :|: z1 >= 0, z0171 >= 0, z = 1 + (1 + z0171 + z1128 + z285) + z1 + z2, z1128 >= 0, z2 >= 0, z285 >= 0 mark(z) -{ 0 }-> a__U12(1, z1, z2) :|: z1 >= 0, z = 1 + 1 + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__U12(0, z1, z2) :|: z1 >= 0, z = 1 + 0 + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__U12(0, z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U12(1 + mark(z0174), z1, z2) :|: z0174 >= 0, z1 >= 0, z = 1 + (1 + z0174) + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__U11(a__plus(mark(z0169), mark(z1127)), z1, z2) :|: z1127 >= 0, z1 >= 0, z = 1 + (1 + z0169 + z1127) + z1 + z2, z0169 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U11(a__U12(mark(z0168), z1126, z284), z1, z2) :|: z0168 >= 0, z1 >= 0, z = 1 + (1 + z0168 + z1126 + z284) + z1 + z2, z284 >= 0, z1126 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U11(a__U11(mark(z0167), z1125, z283), z1, z2) :|: z0167 >= 0, z1 >= 0, z = 1 + (1 + z0167 + z1125 + z283) + z1 + z2, z1125 >= 0, z283 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U11(1, z1, z2) :|: z1 >= 0, z = 1 + 1 + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__U11(0, z1, z2) :|: z1 >= 0, z = 1 + 0 + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__U11(0, z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U11(1 + mark(z0170), z1, z2) :|: z0170 >= 0, z1 >= 0, z = 1 + (1 + z0170) + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> 1 :|: z = 1 mark(z) -{ 0 }-> 0 :|: z = 0 mark(z) -{ 0 }-> 0 :|: z >= 0 mark(z) -{ 0 }-> 1 + mark(z - 1) :|: z - 1 >= 0 ---------------------------------------- (67) CompletionProof (UPPER BOUND(ID)) The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added: a__U11(v0, v1, v2) -> null_a__U11 [0] a__U12(v0, v1, v2) -> null_a__U12 [0] a__plus(v0, v1) -> null_a__plus [0] mark(v0) -> null_mark [0] A__U11(v0, v1, v2) -> null_A__U11 [0] A__U12(v0, v1, v2) -> null_A__U12 [0] A__PLUS(v0, v1) -> null_A__PLUS [0] MARK(v0) -> null_MARK [0] And the following fresh constants: null_a__U11, null_a__U12, null_a__plus, null_mark, null_A__U11, null_A__U12, null_A__PLUS, null_MARK ---------------------------------------- (68) 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, z0, z1) -> c(A__U12(tt, z0, z1)) [1] A__U12(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1)) [1] A__U12(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0)) [1] A__PLUS(z0, 0) -> c5(MARK(z0)) [1] A__PLUS(z0, s(z1)) -> c6(A__U11(tt, z1, z0)) [1] MARK(U11(z0, z1, z2)) -> c8(A__U11(mark(z0), z1, z2), MARK(z0)) [1] MARK(U12(z0, z1, z2)) -> c9(A__U12(mark(z0), z1, z2), MARK(z0)) [1] MARK(plus(z0, z1)) -> c10(A__PLUS(mark(z0), mark(z1)), MARK(z0)) [1] MARK(plus(z0, z1)) -> c11(A__PLUS(mark(z0), mark(z1)), MARK(z1)) [1] MARK(s(z0)) -> c13(MARK(z0)) [1] a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) [0] a__U11(z0, z1, z2) -> U11(z0, z1, z2) [0] a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) [0] a__U12(z0, z1, z2) -> U12(z0, z1, z2) [0] a__plus(z0, 0) -> mark(z0) [0] a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) [0] a__plus(z0, z1) -> plus(z0, z1) [0] mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) [0] mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) [0] mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) [0] mark(tt) -> tt [0] mark(s(z0)) -> s(mark(z0)) [0] mark(0) -> 0 [0] a__U11(v0, v1, v2) -> null_a__U11 [0] a__U12(v0, v1, v2) -> null_a__U12 [0] a__plus(v0, v1) -> null_a__plus [0] mark(v0) -> null_mark [0] A__U11(v0, v1, v2) -> null_A__U11 [0] A__U12(v0, v1, v2) -> null_A__U12 [0] A__PLUS(v0, v1) -> null_A__PLUS [0] MARK(v0) -> null_MARK [0] The TRS has the following type information: A__U11 :: tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> c:null_A__U11 tt :: tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark c :: c2:c3:null_A__U12 -> c:null_A__U11 A__U12 :: tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> c2:c3:null_A__U12 c2 :: c5:c6:null_A__PLUS -> c8:c9:c10:c11:c13:null_MARK -> c2:c3:null_A__U12 A__PLUS :: tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> c5:c6:null_A__PLUS mark :: tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark MARK :: tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> c8:c9:c10:c11:c13:null_MARK c3 :: c5:c6:null_A__PLUS -> c8:c9:c10:c11:c13:null_MARK -> c2:c3:null_A__U12 0 :: tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark c5 :: c8:c9:c10:c11:c13:null_MARK -> c5:c6:null_A__PLUS s :: tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark c6 :: c:null_A__U11 -> c5:c6:null_A__PLUS U11 :: tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark c8 :: c:null_A__U11 -> c8:c9:c10:c11:c13:null_MARK -> c8:c9:c10:c11:c13:null_MARK U12 :: tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark c9 :: c2:c3:null_A__U12 -> c8:c9:c10:c11:c13:null_MARK -> c8:c9:c10:c11:c13:null_MARK plus :: tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark c10 :: c5:c6:null_A__PLUS -> c8:c9:c10:c11:c13:null_MARK -> c8:c9:c10:c11:c13:null_MARK c11 :: c5:c6:null_A__PLUS -> c8:c9:c10:c11:c13:null_MARK -> c8:c9:c10:c11:c13:null_MARK c13 :: c8:c9:c10:c11:c13:null_MARK -> c8:c9:c10:c11:c13:null_MARK a__U11 :: tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark a__U12 :: tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark a__plus :: tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark -> tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark null_a__U11 :: tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark null_a__U12 :: tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark null_a__plus :: tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark null_mark :: tt:0:s:U11:U12:plus:null_a__U11:null_a__U12:null_a__plus:null_mark null_A__U11 :: c:null_A__U11 null_A__U12 :: c2:c3:null_A__U12 null_A__PLUS :: c5:c6:null_A__PLUS null_MARK :: c8:c9:c10:c11:c13:null_MARK Rewrite Strategy: INNERMOST ---------------------------------------- (69) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: tt => 1 0 => 0 null_a__U11 => 0 null_a__U12 => 0 null_a__plus => 0 null_mark => 0 null_A__U11 => 0 null_A__U12 => 0 null_A__PLUS => 0 null_MARK => 0 ---------------------------------------- (70) Obligation: Complexity RNTS consisting of the following rules: A__PLUS(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 A__PLUS(z, z') -{ 1 }-> 1 + MARK(z0) :|: z = z0, z0 >= 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U11(1, z1, z0) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1 A__U11(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 A__U11(z, z', z'') -{ 1 }-> 1 + A__U12(1, z0, z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 A__U12(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 A__U12(z, z', z'') -{ 1 }-> 1 + A__PLUS(mark(z1), mark(z0)) + MARK(z0) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 A__U12(z, z', z'') -{ 1 }-> 1 + A__PLUS(mark(z1), mark(z0)) + MARK(z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 MARK(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__PLUS(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__PLUS(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__U11(z, z', z'') -{ 0 }-> a__U12(1, z0, z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 a__U11(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 a__U11(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 a__U12(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 a__U12(z, z', z'') -{ 0 }-> 1 + a__plus(mark(z1), mark(z0)) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 a__U12(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 a__plus(z, z') -{ 0 }-> mark(z0) :|: z = z0, z0 >= 0, z' = 0 a__plus(z, z') -{ 0 }-> a__U11(1, z1, z0) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1 a__plus(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__plus(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 mark(z) -{ 0 }-> a__plus(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U12(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U11(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> 1 :|: z = 1 mark(z) -{ 0 }-> 0 :|: z = 0 mark(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 mark(z) -{ 0 }-> 1 + mark(z0) :|: z = 1 + z0, z0 >= 0 Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (71) 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)) ---------------------------------------- (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__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 ---------------------------------------- (73) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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__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 ---------------------------------------- (75) 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)) ---------------------------------------- (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(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 ---------------------------------------- (77) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__U12(tt, tt, x1) -> c3(A__PLUS(mark(x1), tt), MARK(tt)) ---------------------------------------- (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(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 ---------------------------------------- (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(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 ---------------------------------------- (81) 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)) ---------------------------------------- (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(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 ---------------------------------------- (83) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(U11(0, x1, x2)) -> c8(A__U11(0, x1, x2), MARK(0)) ---------------------------------------- (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(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 ---------------------------------------- (85) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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(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 ---------------------------------------- (87) 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)) ---------------------------------------- (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(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 ---------------------------------------- (89) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(U12(0, x1, x2)) -> c9(A__U12(0, x1, x2), MARK(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(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 ---------------------------------------- (91) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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(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 ---------------------------------------- (93) 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)) ---------------------------------------- (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(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 ---------------------------------------- (95) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 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(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 ---------------------------------------- (97) 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)) ---------------------------------------- (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, 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 ---------------------------------------- (99) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(plus(x0, tt)) -> c11(A__PLUS(mark(x0), tt), MARK(tt)) ---------------------------------------- (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, 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 ---------------------------------------- (101) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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, 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 ---------------------------------------- (103) 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)) ---------------------------------------- (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, 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 ---------------------------------------- (105) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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, 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 ---------------------------------------- (107) 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)) ---------------------------------------- (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, 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 ---------------------------------------- (109) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 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, 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 ---------------------------------------- (111) 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)) ---------------------------------------- (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, 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 ---------------------------------------- (113) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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, 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 ---------------------------------------- (115) 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))) ---------------------------------------- (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, 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 ---------------------------------------- (117) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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, 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 ---------------------------------------- (119) 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))) ---------------------------------------- (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, 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 ---------------------------------------- (121) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 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, 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 ---------------------------------------- (123) 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))) ---------------------------------------- (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, 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 ---------------------------------------- (125) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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, 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 ---------------------------------------- (127) 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))) ---------------------------------------- (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, 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 ---------------------------------------- (129) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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, 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 ---------------------------------------- (131) 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)) ---------------------------------------- (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, 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, 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)) 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) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__U12(tt, tt, tt) -> c2(A__PLUS(tt, tt)) ---------------------------------------- (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, 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 ---------------------------------------- (135) 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)) ---------------------------------------- (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, 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 ---------------------------------------- (137) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__U12(tt, tt, 0) -> c2(A__PLUS(0, 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, 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 ---------------------------------------- (139) 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))) ---------------------------------------- (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, 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)) -> 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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 ---------------------------------------- (141) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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, 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 ---------------------------------------- (143) 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))) ---------------------------------------- (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, 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))) 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 ---------------------------------------- (145) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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, 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)) 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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 ---------------------------------------- (147) 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))) ---------------------------------------- (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, 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))) 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))) 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) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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, 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))) 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 ---------------------------------------- (151) 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)) ---------------------------------------- (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, 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), 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)) 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 ---------------------------------------- (153) 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)) ---------------------------------------- (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, 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)), 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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, 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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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, 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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)) 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 ---------------------------------------- (155) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 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, 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 ---------------------------------------- (157) 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)) ---------------------------------------- (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, 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))) 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)), 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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), 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 ---------------------------------------- (159) 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)) ---------------------------------------- (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, 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, 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)), 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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)) 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 ---------------------------------------- (161) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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, 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) -> 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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, 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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)) 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 ---------------------------------------- (163) 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)) ---------------------------------------- (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, 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)) -> 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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, 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, 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, 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 ---------------------------------------- (165) 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)) ---------------------------------------- (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, 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)) -> 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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, 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)) 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 ---------------------------------------- (167) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 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, 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, 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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)) 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))) 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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)) 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 ---------------------------------------- (169) 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)) ---------------------------------------- (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, 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, 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))) 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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)) 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 ---------------------------------------- (171) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__U12(tt, tt, tt) -> c3(A__PLUS(tt, tt), MARK(tt)) ---------------------------------------- (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, 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), 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), 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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)) 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 ---------------------------------------- (173) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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, 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)), 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)) 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 ---------------------------------------- (175) 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)) ---------------------------------------- (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, 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)) 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)) -> 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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)) 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 ---------------------------------------- (177) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__U12(tt, tt, s(x1)) -> c3(A__PLUS(s(mark(x1)), tt), MARK(tt)) ---------------------------------------- (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, 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)) 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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 ---------------------------------------- (179) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 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, 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), 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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), 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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)) 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 ---------------------------------------- (181) 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)) ---------------------------------------- (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(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) -> 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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, 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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 ---------------------------------------- (183) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__U12(tt, tt, 0) -> c3(A__PLUS(0, tt), MARK(tt)) ---------------------------------------- (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(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)), 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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))) 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)), 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))) 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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(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 ---------------------------------------- (185) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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(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)), 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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, 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, 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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)) 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 ---------------------------------------- (187) 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))) ---------------------------------------- (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(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)) -> 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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 ---------------------------------------- (189) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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(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 ---------------------------------------- (191) 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))) ---------------------------------------- (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(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 ---------------------------------------- (193) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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(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 ---------------------------------------- (195) 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))) ---------------------------------------- (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(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 ---------------------------------------- (197) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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(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 ---------------------------------------- (199) 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))) ---------------------------------------- (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(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 ---------------------------------------- (201) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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(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 ---------------------------------------- (203) 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))) ---------------------------------------- (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(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 ---------------------------------------- (205) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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(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 ---------------------------------------- (207) 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))) ---------------------------------------- (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, 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 ---------------------------------------- (209) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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, 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 ---------------------------------------- (211) 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)) ---------------------------------------- (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, 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 ---------------------------------------- (213) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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, 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 ---------------------------------------- (215) 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)) ---------------------------------------- (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, 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 ---------------------------------------- (217) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 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, 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 ---------------------------------------- (219) 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)) ---------------------------------------- (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(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 ---------------------------------------- (221) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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(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 ---------------------------------------- (223) 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))) ---------------------------------------- (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(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 ---------------------------------------- (225) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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(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 ---------------------------------------- (227) 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))) ---------------------------------------- (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(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 ---------------------------------------- (229) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 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(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 ---------------------------------------- (231) 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))) ---------------------------------------- (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(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 ---------------------------------------- (233) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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(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 ---------------------------------------- (235) 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))) ---------------------------------------- (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(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 ---------------------------------------- (237) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (238) 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 ---------------------------------------- (239) 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)) ---------------------------------------- (240) 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 ---------------------------------------- (241) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(plus(tt, tt)) -> c10(A__PLUS(tt, tt)) ---------------------------------------- (242) 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 ---------------------------------------- (243) 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)) ---------------------------------------- (244) 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 ---------------------------------------- (245) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(plus(0, tt)) -> c10(A__PLUS(0, tt)) ---------------------------------------- (246) 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 ---------------------------------------- (247) 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))) ---------------------------------------- (248) 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 ---------------------------------------- (249) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (250) 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 ---------------------------------------- (251) 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))) ---------------------------------------- (252) 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 ---------------------------------------- (253) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (254) 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 ---------------------------------------- (255) 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))) ---------------------------------------- (256) 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 ---------------------------------------- (257) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (258) 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 ---------------------------------------- (259) 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)) ---------------------------------------- (260) 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 ---------------------------------------- (261) 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)) ---------------------------------------- (262) 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 ---------------------------------------- (263) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (264) 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 ---------------------------------------- (265) 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)) ---------------------------------------- (266) 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 ---------------------------------------- (267) 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)) ---------------------------------------- (268) 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 ---------------------------------------- (269) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (270) 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 ---------------------------------------- (271) 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)) ---------------------------------------- (272) 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 ---------------------------------------- (273) 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)) ---------------------------------------- (274) 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 ---------------------------------------- (275) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (276) 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 ---------------------------------------- (277) 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)) ---------------------------------------- (278) 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 ---------------------------------------- (279) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(plus(tt, tt)) -> c11(A__PLUS(tt, tt), MARK(tt)) ---------------------------------------- (280) 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 ---------------------------------------- (281) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (282) 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 ---------------------------------------- (283) RelTrsToWeightedTrsProof (UPPER BOUND(ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (284) 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 ---------------------------------------- (285) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (286) 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 ---------------------------------------- (287) 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 ---------------------------------------- (288) 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 ---------------------------------------- (289) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (290) 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 ---------------------------------------- (291) 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 ---------------------------------------- (292) 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 ---------------------------------------- (293) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (294) 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 ---------------------------------------- (295) 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 ---------------------------------------- (296) 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 ---------------------------------------- (297) 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 ---------------------------------------- (298) 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.