KILLED proof of input_lHZSRTLKwJ.trs # AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF).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), 61 ms] (6) CdtProblem (7) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxRelTRS (9) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (10) TRS for Loop Detection (11) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CpxRelTRS (13) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (14) typed CpxTrs (15) OrderProof [LOWER BOUND(ID), 0 ms] (16) typed CpxTrs (17) RewriteLemmaProof [LOWER BOUND(ID), 8919 ms] (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 617 ms] (20) typed CpxTrs (21) RewriteLemmaProof [LOWER BOUND(ID), 56 ms] (22) typed CpxTrs (23) RelTrsToWeightedTrsProof [UPPER BOUND(ID), 0 ms] (24) CpxWeightedTrs (25) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (26) CpxTypedWeightedTrs (27) CompletionProof [UPPER BOUND(ID), 0 ms] (28) CpxTypedWeightedCompleteTrs (29) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 6 ms] (30) CpxRNTS (31) CompletionProof [UPPER BOUND(ID), 0 ms] (32) CpxTypedWeightedCompleteTrs (33) NarrowingProof [BOTH BOUNDS(ID, ID), 356 ms] (34) CpxTypedWeightedCompleteTrs (35) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (36) CpxRNTS (37) InliningProof [UPPER BOUND(ID), 472 ms] (38) CpxRNTS (39) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (40) CpxRNTS (41) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (42) CdtProblem (43) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (44) CdtProblem (45) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (46) CdtProblem (47) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (48) CpxRelTRS (49) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (50) CpxTRS (51) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (52) CpxWeightedTrs (53) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (54) CpxTypedWeightedTrs (55) CompletionProof [UPPER BOUND(ID), 0 ms] (56) CpxTypedWeightedCompleteTrs (57) NarrowingProof [BOTH BOUNDS(ID, ID), 58.3 s] (58) CpxTypedWeightedCompleteTrs (59) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (60) CpxRNTS (61) InliningProof [UPPER BOUND(ID), 1176 ms] (62) CpxRNTS (63) SimplificationProof [BOTH BOUNDS(ID, ID), 1 ms] (64) CpxRNTS (65) CompletionProof [UPPER BOUND(ID), 0 ms] (66) CpxTypedWeightedCompleteTrs (67) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (68) CpxRNTS (69) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (70) CdtProblem (71) CdtLeafRemovalProof [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) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (78) CdtProblem (79) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 6 ms] (80) CdtProblem (81) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (82) CdtProblem (83) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (84) CdtProblem (85) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 60 ms] (86) CdtProblem (87) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 14 ms] (88) CdtProblem (89) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 83 ms] (90) CdtProblem (91) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 18 ms] (92) CdtProblem (93) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 8 ms] (94) CdtProblem (95) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (96) CdtProblem (97) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (98) CdtProblem (99) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (100) CdtProblem (101) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (102) CdtProblem (103) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 69 ms] (104) CdtProblem (105) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 14 ms] (106) CdtProblem (107) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 8 ms] (108) CdtProblem (109) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 3 ms] (110) CdtProblem (111) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 65 ms] (112) CdtProblem (113) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 1 ms] (114) CdtProblem (115) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (116) CdtProblem (117) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 41 ms] (118) CdtProblem (119) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 19 ms] (120) CdtProblem (121) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 8 ms] (122) CdtProblem (123) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (124) CdtProblem (125) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 101 ms] (126) CdtProblem (127) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (128) CdtProblem (129) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 13 ms] (130) CdtProblem (131) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 121 ms] (132) CdtProblem (133) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 21 ms] (134) CdtProblem (135) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (136) CdtProblem (137) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 88 ms] (138) CdtProblem (139) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (140) CdtProblem (141) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (142) CdtProblem (143) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 219 ms] (144) CdtProblem (145) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 19 ms] (146) CdtProblem (147) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 8 ms] (148) CdtProblem (149) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 141 ms] (150) CdtProblem (151) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 9 ms] (152) CdtProblem (153) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 31 ms] (154) CdtProblem (155) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 220 ms] (156) CdtProblem (157) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 30 ms] (158) CdtProblem (159) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 30 ms] (160) CdtProblem (161) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 117 ms] (162) CdtProblem (163) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 23 ms] (164) CdtProblem (165) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 21 ms] (166) CdtProblem (167) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 55 ms] (168) CdtProblem (169) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (170) CdtProblem (171) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 10 ms] (172) CdtProblem (173) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 78 ms] (174) CdtProblem (175) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 17 ms] (176) CdtProblem (177) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 13 ms] (178) CdtProblem (179) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 72 ms] (180) CdtProblem (181) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 43 ms] (182) CdtProblem (183) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 35 ms] (184) CdtProblem (185) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 191 ms] (186) CdtProblem (187) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 14 ms] (188) CdtProblem (189) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 220 ms] (190) CdtProblem (191) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 24 ms] (192) CdtProblem (193) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 231 ms] (194) CdtProblem (195) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 39 ms] (196) CdtProblem (197) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 422 ms] (198) CdtProblem (199) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 25 ms] (200) CdtProblem (201) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 265 ms] (202) CdtProblem (203) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 48 ms] (204) CdtProblem (205) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 435 ms] (206) CdtProblem (207) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 64 ms] (208) CdtProblem (209) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 314 ms] (210) CdtProblem (211) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 373 ms] (212) CdtProblem (213) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 91 ms] (214) CdtProblem (215) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 359 ms] (216) CdtProblem (217) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 78 ms] (218) CdtProblem (219) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 320 ms] (220) CdtProblem (221) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 80 ms] (222) CdtProblem (223) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 511 ms] (224) CdtProblem (225) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 90 ms] (226) CdtProblem (227) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 447 ms] (228) CdtProblem (229) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 133 ms] (230) CdtProblem (231) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 576 ms] (232) CdtProblem (233) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 87 ms] (234) CdtProblem ---------------------------------------- (0) Obligation: The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: a__fact(X) -> a__if(a__zero(mark(X)), s(0), prod(X, fact(p(X)))) a__add(0, X) -> mark(X) a__add(s(X), Y) -> s(a__add(mark(X), mark(Y))) a__prod(0, X) -> 0 a__prod(s(X), Y) -> a__add(mark(Y), a__prod(mark(X), mark(Y))) a__if(true, X, Y) -> mark(X) a__if(false, X, Y) -> mark(Y) a__zero(0) -> true a__zero(s(X)) -> false a__p(s(X)) -> mark(X) mark(fact(X)) -> a__fact(mark(X)) mark(if(X1, X2, X3)) -> a__if(mark(X1), X2, X3) mark(zero(X)) -> a__zero(mark(X)) mark(prod(X1, X2)) -> a__prod(mark(X1), mark(X2)) mark(p(X)) -> a__p(mark(X)) mark(add(X1, X2)) -> a__add(mark(X1), mark(X2)) mark(s(X)) -> s(mark(X)) mark(0) -> 0 mark(true) -> true mark(false) -> false a__fact(X) -> fact(X) a__if(X1, X2, X3) -> if(X1, X2, X3) a__zero(X) -> zero(X) a__prod(X1, X2) -> prod(X1, X2) a__p(X) -> p(X) a__add(X1, X2) -> add(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__fact(X) -> a__if(a__zero(mark(X)), s(0'), prod(X, fact(p(X)))) a__add(0', X) -> mark(X) a__add(s(X), Y) -> s(a__add(mark(X), mark(Y))) a__prod(0', X) -> 0' a__prod(s(X), Y) -> a__add(mark(Y), a__prod(mark(X), mark(Y))) a__if(true, X, Y) -> mark(X) a__if(false, X, Y) -> mark(Y) a__zero(0') -> true a__zero(s(X)) -> false a__p(s(X)) -> mark(X) mark(fact(X)) -> a__fact(mark(X)) mark(if(X1, X2, X3)) -> a__if(mark(X1), X2, X3) mark(zero(X)) -> a__zero(mark(X)) mark(prod(X1, X2)) -> a__prod(mark(X1), mark(X2)) mark(p(X)) -> a__p(mark(X)) mark(add(X1, X2)) -> a__add(mark(X1), mark(X2)) mark(s(X)) -> s(mark(X)) mark(0') -> 0' mark(true) -> true mark(false) -> false a__fact(X) -> fact(X) a__if(X1, X2, X3) -> if(X1, X2, X3) a__zero(X) -> zero(X) a__prod(X1, X2) -> prod(X1, X2) a__p(X) -> p(X) a__add(X1, X2) -> add(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__fact(X) -> a__if(a__zero(mark(X)), s(0), prod(X, fact(p(X)))) a__add(0, X) -> mark(X) a__add(s(X), Y) -> s(a__add(mark(X), mark(Y))) a__prod(0, X) -> 0 a__prod(s(X), Y) -> a__add(mark(Y), a__prod(mark(X), mark(Y))) a__if(true, X, Y) -> mark(X) a__if(false, X, Y) -> mark(Y) a__zero(0) -> true a__zero(s(X)) -> false a__p(s(X)) -> mark(X) mark(fact(X)) -> a__fact(mark(X)) mark(if(X1, X2, X3)) -> a__if(mark(X1), X2, X3) mark(zero(X)) -> a__zero(mark(X)) mark(prod(X1, X2)) -> a__prod(mark(X1), mark(X2)) mark(p(X)) -> a__p(mark(X)) mark(add(X1, X2)) -> a__add(mark(X1), mark(X2)) mark(s(X)) -> s(mark(X)) mark(0) -> 0 mark(true) -> true mark(false) -> false a__fact(X) -> fact(X) a__if(X1, X2, X3) -> if(X1, X2, X3) a__zero(X) -> zero(X) a__prod(X1, X2) -> prod(X1, X2) a__p(X) -> p(X) a__add(X1, X2) -> add(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__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), A__ZERO(mark(z0)), MARK(z0)) A__FACT(z0) -> c1 A__ADD(0, z0) -> c2(MARK(z0)) A__ADD(s(z0), z1) -> c3(A__ADD(mark(z0), mark(z1)), MARK(z0)) A__ADD(s(z0), z1) -> c4(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__ADD(z0, z1) -> c5 A__PROD(0, z0) -> c6 A__PROD(s(z0), z1) -> c7(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), MARK(z1)) A__PROD(s(z0), z1) -> c8(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z0)) A__PROD(s(z0), z1) -> c9(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z1)) A__PROD(z0, z1) -> c10 A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__IF(z0, z1, z2) -> c13 A__ZERO(0) -> c14 A__ZERO(s(z0)) -> c15 A__ZERO(z0) -> c16 A__P(s(z0)) -> c17(MARK(z0)) A__P(z0) -> c18 MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(if(z0, z1, z2)) -> c20(A__IF(mark(z0), z1, z2), MARK(z0)) MARK(zero(z0)) -> c21(A__ZERO(mark(z0)), MARK(z0)) MARK(prod(z0, z1)) -> c22(A__PROD(mark(z0), mark(z1)), MARK(z0)) MARK(prod(z0, z1)) -> c23(A__PROD(mark(z0), mark(z1)), MARK(z1)) MARK(p(z0)) -> c24(A__P(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) MARK(0) -> c28 MARK(true) -> c29 MARK(false) -> c30 S tuples: A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), A__ZERO(mark(z0)), MARK(z0)) A__FACT(z0) -> c1 A__ADD(0, z0) -> c2(MARK(z0)) A__ADD(s(z0), z1) -> c3(A__ADD(mark(z0), mark(z1)), MARK(z0)) A__ADD(s(z0), z1) -> c4(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__ADD(z0, z1) -> c5 A__PROD(0, z0) -> c6 A__PROD(s(z0), z1) -> c7(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), MARK(z1)) A__PROD(s(z0), z1) -> c8(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z0)) A__PROD(s(z0), z1) -> c9(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z1)) A__PROD(z0, z1) -> c10 A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__IF(z0, z1, z2) -> c13 A__ZERO(0) -> c14 A__ZERO(s(z0)) -> c15 A__ZERO(z0) -> c16 A__P(s(z0)) -> c17(MARK(z0)) A__P(z0) -> c18 MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(if(z0, z1, z2)) -> c20(A__IF(mark(z0), z1, z2), MARK(z0)) MARK(zero(z0)) -> c21(A__ZERO(mark(z0)), MARK(z0)) MARK(prod(z0, z1)) -> c22(A__PROD(mark(z0), mark(z1)), MARK(z0)) MARK(prod(z0, z1)) -> c23(A__PROD(mark(z0), mark(z1)), MARK(z1)) MARK(p(z0)) -> c24(A__P(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) MARK(0) -> c28 MARK(true) -> c29 MARK(false) -> c30 K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__FACT_1, A__ADD_2, A__PROD_2, A__IF_3, A__ZERO_1, A__P_1, MARK_1 Compound Symbols: c_3, c1, c2_1, c3_2, c4_2, c5, c6, c7_2, c8_3, c9_3, c10, c11_1, c12_1, c13, c14, c15, c16, c17_1, c18, c19_2, c20_2, c21_2, c22_2, c23_2, c24_2, c25_2, c26_2, c27_1, c28, c29, c30 ---------------------------------------- (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(1, INF). The TRS R consists of the following rules: A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), A__ZERO(mark(z0)), MARK(z0)) A__FACT(z0) -> c1 A__ADD(0, z0) -> c2(MARK(z0)) A__ADD(s(z0), z1) -> c3(A__ADD(mark(z0), mark(z1)), MARK(z0)) A__ADD(s(z0), z1) -> c4(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__ADD(z0, z1) -> c5 A__PROD(0, z0) -> c6 A__PROD(s(z0), z1) -> c7(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), MARK(z1)) A__PROD(s(z0), z1) -> c8(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z0)) A__PROD(s(z0), z1) -> c9(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z1)) A__PROD(z0, z1) -> c10 A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__IF(z0, z1, z2) -> c13 A__ZERO(0) -> c14 A__ZERO(s(z0)) -> c15 A__ZERO(z0) -> c16 A__P(s(z0)) -> c17(MARK(z0)) A__P(z0) -> c18 MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(if(z0, z1, z2)) -> c20(A__IF(mark(z0), z1, z2), MARK(z0)) MARK(zero(z0)) -> c21(A__ZERO(mark(z0)), MARK(z0)) MARK(prod(z0, z1)) -> c22(A__PROD(mark(z0), mark(z1)), MARK(z0)) MARK(prod(z0, z1)) -> c23(A__PROD(mark(z0), mark(z1)), MARK(z1)) MARK(p(z0)) -> c24(A__P(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) MARK(0) -> c28 MARK(true) -> c29 MARK(false) -> c30 The (relative) TRS S consists of the following rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Rewrite Strategy: INNERMOST ---------------------------------------- (9) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) Transformed a relative TRS into a decreasing-loop problem. ---------------------------------------- (10) Obligation: Analyzing the following TRS for decreasing loops: 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__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), A__ZERO(mark(z0)), MARK(z0)) A__FACT(z0) -> c1 A__ADD(0, z0) -> c2(MARK(z0)) A__ADD(s(z0), z1) -> c3(A__ADD(mark(z0), mark(z1)), MARK(z0)) A__ADD(s(z0), z1) -> c4(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__ADD(z0, z1) -> c5 A__PROD(0, z0) -> c6 A__PROD(s(z0), z1) -> c7(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), MARK(z1)) A__PROD(s(z0), z1) -> c8(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z0)) A__PROD(s(z0), z1) -> c9(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z1)) A__PROD(z0, z1) -> c10 A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__IF(z0, z1, z2) -> c13 A__ZERO(0) -> c14 A__ZERO(s(z0)) -> c15 A__ZERO(z0) -> c16 A__P(s(z0)) -> c17(MARK(z0)) A__P(z0) -> c18 MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(if(z0, z1, z2)) -> c20(A__IF(mark(z0), z1, z2), MARK(z0)) MARK(zero(z0)) -> c21(A__ZERO(mark(z0)), MARK(z0)) MARK(prod(z0, z1)) -> c22(A__PROD(mark(z0), mark(z1)), MARK(z0)) MARK(prod(z0, z1)) -> c23(A__PROD(mark(z0), mark(z1)), MARK(z1)) MARK(p(z0)) -> c24(A__P(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) MARK(0) -> c28 MARK(true) -> c29 MARK(false) -> c30 The (relative) TRS S consists of the following rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Rewrite Strategy: INNERMOST ---------------------------------------- (11) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (12) 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__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0'), prod(z0, fact(p(z0)))), A__ZERO(mark(z0)), MARK(z0)) A__FACT(z0) -> c1 A__ADD(0', z0) -> c2(MARK(z0)) A__ADD(s(z0), z1) -> c3(A__ADD(mark(z0), mark(z1)), MARK(z0)) A__ADD(s(z0), z1) -> c4(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__ADD(z0, z1) -> c5 A__PROD(0', z0) -> c6 A__PROD(s(z0), z1) -> c7(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), MARK(z1)) A__PROD(s(z0), z1) -> c8(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z0)) A__PROD(s(z0), z1) -> c9(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z1)) A__PROD(z0, z1) -> c10 A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__IF(z0, z1, z2) -> c13 A__ZERO(0') -> c14 A__ZERO(s(z0)) -> c15 A__ZERO(z0) -> c16 A__P(s(z0)) -> c17(MARK(z0)) A__P(z0) -> c18 MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(if(z0, z1, z2)) -> c20(A__IF(mark(z0), z1, z2), MARK(z0)) MARK(zero(z0)) -> c21(A__ZERO(mark(z0)), MARK(z0)) MARK(prod(z0, z1)) -> c22(A__PROD(mark(z0), mark(z1)), MARK(z0)) MARK(prod(z0, z1)) -> c23(A__PROD(mark(z0), mark(z1)), MARK(z1)) MARK(p(z0)) -> c24(A__P(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) MARK(0') -> c28 MARK(true) -> c29 MARK(false) -> c30 The (relative) TRS S consists of the following rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0'), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0', z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0', z0) -> 0' a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0') -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0') -> 0' mark(true) -> true mark(false) -> false Rewrite Strategy: INNERMOST ---------------------------------------- (13) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Inferred types. ---------------------------------------- (14) Obligation: Innermost TRS: Rules: A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0'), prod(z0, fact(p(z0)))), A__ZERO(mark(z0)), MARK(z0)) A__FACT(z0) -> c1 A__ADD(0', z0) -> c2(MARK(z0)) A__ADD(s(z0), z1) -> c3(A__ADD(mark(z0), mark(z1)), MARK(z0)) A__ADD(s(z0), z1) -> c4(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__ADD(z0, z1) -> c5 A__PROD(0', z0) -> c6 A__PROD(s(z0), z1) -> c7(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), MARK(z1)) A__PROD(s(z0), z1) -> c8(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z0)) A__PROD(s(z0), z1) -> c9(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z1)) A__PROD(z0, z1) -> c10 A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__IF(z0, z1, z2) -> c13 A__ZERO(0') -> c14 A__ZERO(s(z0)) -> c15 A__ZERO(z0) -> c16 A__P(s(z0)) -> c17(MARK(z0)) A__P(z0) -> c18 MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(if(z0, z1, z2)) -> c20(A__IF(mark(z0), z1, z2), MARK(z0)) MARK(zero(z0)) -> c21(A__ZERO(mark(z0)), MARK(z0)) MARK(prod(z0, z1)) -> c22(A__PROD(mark(z0), mark(z1)), MARK(z0)) MARK(prod(z0, z1)) -> c23(A__PROD(mark(z0), mark(z1)), MARK(z1)) MARK(p(z0)) -> c24(A__P(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) MARK(0') -> c28 MARK(true) -> c29 MARK(false) -> c30 a__fact(z0) -> a__if(a__zero(mark(z0)), s(0'), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0', z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0', z0) -> 0' a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0') -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0') -> 0' mark(true) -> true mark(false) -> false Types: A__FACT :: 0':s:p:fact:prod:true:false:if:zero:add -> c:c1 c :: c11:c12:c13 -> c14:c15:c16 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c:c1 A__IF :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add -> c11:c12:c13 a__zero :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add mark :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add s :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add 0' :: 0':s:p:fact:prod:true:false:if:zero:add prod :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add fact :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add p :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add A__ZERO :: 0':s:p:fact:prod:true:false:if:zero:add -> c14:c15:c16 MARK :: 0':s:p:fact:prod:true:false:if:zero:add -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 c1 :: c:c1 A__ADD :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add -> c2:c3:c4:c5 c2 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c2:c3:c4:c5 c3 :: c2:c3:c4:c5 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c2:c3:c4:c5 c4 :: c2:c3:c4:c5 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c2:c3:c4:c5 c5 :: c2:c3:c4:c5 A__PROD :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add -> c6:c7:c8:c9:c10 c6 :: c6:c7:c8:c9:c10 c7 :: c2:c3:c4:c5 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c6:c7:c8:c9:c10 a__prod :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add c8 :: c2:c3:c4:c5 -> c6:c7:c8:c9:c10 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c6:c7:c8:c9:c10 c9 :: c2:c3:c4:c5 -> c6:c7:c8:c9:c10 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c6:c7:c8:c9:c10 c10 :: c6:c7:c8:c9:c10 true :: 0':s:p:fact:prod:true:false:if:zero:add c11 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c11:c12:c13 false :: 0':s:p:fact:prod:true:false:if:zero:add c12 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c11:c12:c13 c13 :: c11:c12:c13 c14 :: c14:c15:c16 c15 :: c14:c15:c16 c16 :: c14:c15:c16 A__P :: 0':s:p:fact:prod:true:false:if:zero:add -> c17:c18 c17 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c17:c18 c18 :: c17:c18 c19 :: c:c1 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 if :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add c20 :: c11:c12:c13 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 zero :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add c21 :: c14:c15:c16 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 c22 :: c6:c7:c8:c9:c10 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 c23 :: c6:c7:c8:c9:c10 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 c24 :: c17:c18 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 add :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add c25 :: c2:c3:c4:c5 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 c26 :: c2:c3:c4:c5 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 c27 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 c28 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 c29 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 c30 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 a__fact :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add a__if :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add a__add :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add a__p :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add hole_c:c11_31 :: c:c1 hole_0':s:p:fact:prod:true:false:if:zero:add2_31 :: 0':s:p:fact:prod:true:false:if:zero:add hole_c11:c12:c133_31 :: c11:c12:c13 hole_c14:c15:c164_31 :: c14:c15:c16 hole_c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c305_31 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 hole_c2:c3:c4:c56_31 :: c2:c3:c4:c5 hole_c6:c7:c8:c9:c107_31 :: c6:c7:c8:c9:c10 hole_c17:c188_31 :: c17:c18 gen_0':s:p:fact:prod:true:false:if:zero:add9_31 :: Nat -> 0':s:p:fact:prod:true:false:if:zero:add gen_c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c3010_31 :: Nat -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 gen_c2:c3:c4:c511_31 :: Nat -> c2:c3:c4:c5 gen_c6:c7:c8:c9:c1012_31 :: Nat -> c6:c7:c8:c9:c10 ---------------------------------------- (15) OrderProof (LOWER BOUND(ID)) Heuristically decided to analyse the following defined symbols: A__FACT, A__IF, mark, MARK, A__ADD, A__PROD, a__prod, A__P, a__fact, a__if, a__add, a__p They will be analysed ascendingly in the following order: A__FACT = A__IF mark < A__FACT A__FACT = MARK A__FACT = A__ADD A__FACT = A__PROD A__FACT = A__P A__IF = MARK A__IF = A__ADD A__IF = A__PROD A__IF = A__P mark < MARK mark < A__ADD mark < A__PROD mark = a__prod mark = a__fact mark = a__if mark = a__add mark = a__p MARK = A__ADD MARK = A__PROD MARK = A__P A__ADD = A__PROD A__ADD = A__P a__prod < A__PROD A__PROD = A__P a__prod = a__fact a__prod = a__if a__prod = a__add a__prod = a__p a__fact = a__if a__fact = a__add a__fact = a__p a__if = a__add a__if = a__p a__add = a__p ---------------------------------------- (16) Obligation: Innermost TRS: Rules: A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0'), prod(z0, fact(p(z0)))), A__ZERO(mark(z0)), MARK(z0)) A__FACT(z0) -> c1 A__ADD(0', z0) -> c2(MARK(z0)) A__ADD(s(z0), z1) -> c3(A__ADD(mark(z0), mark(z1)), MARK(z0)) A__ADD(s(z0), z1) -> c4(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__ADD(z0, z1) -> c5 A__PROD(0', z0) -> c6 A__PROD(s(z0), z1) -> c7(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), MARK(z1)) A__PROD(s(z0), z1) -> c8(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z0)) A__PROD(s(z0), z1) -> c9(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z1)) A__PROD(z0, z1) -> c10 A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__IF(z0, z1, z2) -> c13 A__ZERO(0') -> c14 A__ZERO(s(z0)) -> c15 A__ZERO(z0) -> c16 A__P(s(z0)) -> c17(MARK(z0)) A__P(z0) -> c18 MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(if(z0, z1, z2)) -> c20(A__IF(mark(z0), z1, z2), MARK(z0)) MARK(zero(z0)) -> c21(A__ZERO(mark(z0)), MARK(z0)) MARK(prod(z0, z1)) -> c22(A__PROD(mark(z0), mark(z1)), MARK(z0)) MARK(prod(z0, z1)) -> c23(A__PROD(mark(z0), mark(z1)), MARK(z1)) MARK(p(z0)) -> c24(A__P(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) MARK(0') -> c28 MARK(true) -> c29 MARK(false) -> c30 a__fact(z0) -> a__if(a__zero(mark(z0)), s(0'), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0', z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0', z0) -> 0' a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0') -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0') -> 0' mark(true) -> true mark(false) -> false Types: A__FACT :: 0':s:p:fact:prod:true:false:if:zero:add -> c:c1 c :: c11:c12:c13 -> c14:c15:c16 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c:c1 A__IF :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add -> c11:c12:c13 a__zero :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add mark :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add s :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add 0' :: 0':s:p:fact:prod:true:false:if:zero:add prod :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add fact :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add p :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add A__ZERO :: 0':s:p:fact:prod:true:false:if:zero:add -> c14:c15:c16 MARK :: 0':s:p:fact:prod:true:false:if:zero:add -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 c1 :: c:c1 A__ADD :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add -> c2:c3:c4:c5 c2 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c2:c3:c4:c5 c3 :: c2:c3:c4:c5 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c2:c3:c4:c5 c4 :: c2:c3:c4:c5 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c2:c3:c4:c5 c5 :: c2:c3:c4:c5 A__PROD :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add -> c6:c7:c8:c9:c10 c6 :: c6:c7:c8:c9:c10 c7 :: c2:c3:c4:c5 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c6:c7:c8:c9:c10 a__prod :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add c8 :: c2:c3:c4:c5 -> c6:c7:c8:c9:c10 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c6:c7:c8:c9:c10 c9 :: c2:c3:c4:c5 -> c6:c7:c8:c9:c10 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c6:c7:c8:c9:c10 c10 :: c6:c7:c8:c9:c10 true :: 0':s:p:fact:prod:true:false:if:zero:add c11 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c11:c12:c13 false :: 0':s:p:fact:prod:true:false:if:zero:add c12 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c11:c12:c13 c13 :: c11:c12:c13 c14 :: c14:c15:c16 c15 :: c14:c15:c16 c16 :: c14:c15:c16 A__P :: 0':s:p:fact:prod:true:false:if:zero:add -> c17:c18 c17 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c17:c18 c18 :: c17:c18 c19 :: c:c1 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 if :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add c20 :: c11:c12:c13 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 zero :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add c21 :: c14:c15:c16 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 c22 :: c6:c7:c8:c9:c10 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 c23 :: c6:c7:c8:c9:c10 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 c24 :: c17:c18 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 add :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add c25 :: c2:c3:c4:c5 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 c26 :: c2:c3:c4:c5 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 c27 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 c28 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 c29 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 c30 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 a__fact :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add a__if :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add a__add :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add a__p :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add hole_c:c11_31 :: c:c1 hole_0':s:p:fact:prod:true:false:if:zero:add2_31 :: 0':s:p:fact:prod:true:false:if:zero:add hole_c11:c12:c133_31 :: c11:c12:c13 hole_c14:c15:c164_31 :: c14:c15:c16 hole_c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c305_31 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 hole_c2:c3:c4:c56_31 :: c2:c3:c4:c5 hole_c6:c7:c8:c9:c107_31 :: c6:c7:c8:c9:c10 hole_c17:c188_31 :: c17:c18 gen_0':s:p:fact:prod:true:false:if:zero:add9_31 :: Nat -> 0':s:p:fact:prod:true:false:if:zero:add gen_c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c3010_31 :: Nat -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 gen_c2:c3:c4:c511_31 :: Nat -> c2:c3:c4:c5 gen_c6:c7:c8:c9:c1012_31 :: Nat -> c6:c7:c8:c9:c10 Generator Equations: gen_0':s:p:fact:prod:true:false:if:zero:add9_31(0) <=> 0' gen_0':s:p:fact:prod:true:false:if:zero:add9_31(+(x, 1)) <=> s(gen_0':s:p:fact:prod:true:false:if:zero:add9_31(x)) gen_c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c3010_31(0) <=> c28 gen_c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c3010_31(+(x, 1)) <=> c19(c(c11(c28), c14, c28), gen_c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c3010_31(x)) gen_c2:c3:c4:c511_31(0) <=> c2(c28) gen_c2:c3:c4:c511_31(+(x, 1)) <=> c3(gen_c2:c3:c4:c511_31(x), c28) gen_c6:c7:c8:c9:c1012_31(0) <=> c6 gen_c6:c7:c8:c9:c1012_31(+(x, 1)) <=> c8(c2(c28), gen_c6:c7:c8:c9:c1012_31(x), c28) The following defined symbols remain to be analysed: a__fact, A__FACT, A__IF, mark, MARK, A__ADD, A__PROD, a__prod, A__P, a__if, a__add, a__p They will be analysed ascendingly in the following order: A__FACT = A__IF mark < A__FACT A__FACT = MARK A__FACT = A__ADD A__FACT = A__PROD A__FACT = A__P A__IF = MARK A__IF = A__ADD A__IF = A__PROD A__IF = A__P mark < MARK mark < A__ADD mark < A__PROD mark = a__prod mark = a__fact mark = a__if mark = a__add mark = a__p MARK = A__ADD MARK = A__PROD MARK = A__P A__ADD = A__PROD A__ADD = A__P a__prod < A__PROD A__PROD = A__P a__prod = a__fact a__prod = a__if a__prod = a__add a__prod = a__p a__fact = a__if a__fact = a__add a__fact = a__p a__if = a__add a__if = a__p a__add = a__p ---------------------------------------- (17) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: mark(gen_0':s:p:fact:prod:true:false:if:zero:add9_31(n303395_31)) -> gen_0':s:p:fact:prod:true:false:if:zero:add9_31(n303395_31), rt in Omega(0) Induction Base: mark(gen_0':s:p:fact:prod:true:false:if:zero:add9_31(0)) ->_R^Omega(0) 0' Induction Step: mark(gen_0':s:p:fact:prod:true:false:if:zero:add9_31(+(n303395_31, 1))) ->_R^Omega(0) s(mark(gen_0':s:p:fact:prod:true:false:if:zero:add9_31(n303395_31))) ->_IH s(gen_0':s:p:fact:prod:true:false:if:zero:add9_31(c303396_31)) 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__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0'), prod(z0, fact(p(z0)))), A__ZERO(mark(z0)), MARK(z0)) A__FACT(z0) -> c1 A__ADD(0', z0) -> c2(MARK(z0)) A__ADD(s(z0), z1) -> c3(A__ADD(mark(z0), mark(z1)), MARK(z0)) A__ADD(s(z0), z1) -> c4(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__ADD(z0, z1) -> c5 A__PROD(0', z0) -> c6 A__PROD(s(z0), z1) -> c7(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), MARK(z1)) A__PROD(s(z0), z1) -> c8(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z0)) A__PROD(s(z0), z1) -> c9(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z1)) A__PROD(z0, z1) -> c10 A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__IF(z0, z1, z2) -> c13 A__ZERO(0') -> c14 A__ZERO(s(z0)) -> c15 A__ZERO(z0) -> c16 A__P(s(z0)) -> c17(MARK(z0)) A__P(z0) -> c18 MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(if(z0, z1, z2)) -> c20(A__IF(mark(z0), z1, z2), MARK(z0)) MARK(zero(z0)) -> c21(A__ZERO(mark(z0)), MARK(z0)) MARK(prod(z0, z1)) -> c22(A__PROD(mark(z0), mark(z1)), MARK(z0)) MARK(prod(z0, z1)) -> c23(A__PROD(mark(z0), mark(z1)), MARK(z1)) MARK(p(z0)) -> c24(A__P(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) MARK(0') -> c28 MARK(true) -> c29 MARK(false) -> c30 a__fact(z0) -> a__if(a__zero(mark(z0)), s(0'), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0', z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0', z0) -> 0' a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0') -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0') -> 0' mark(true) -> true mark(false) -> false Types: A__FACT :: 0':s:p:fact:prod:true:false:if:zero:add -> c:c1 c :: c11:c12:c13 -> c14:c15:c16 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c:c1 A__IF :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add -> c11:c12:c13 a__zero :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add mark :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add s :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add 0' :: 0':s:p:fact:prod:true:false:if:zero:add prod :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add fact :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add p :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add A__ZERO :: 0':s:p:fact:prod:true:false:if:zero:add -> c14:c15:c16 MARK :: 0':s:p:fact:prod:true:false:if:zero:add -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 c1 :: c:c1 A__ADD :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add -> c2:c3:c4:c5 c2 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c2:c3:c4:c5 c3 :: c2:c3:c4:c5 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c2:c3:c4:c5 c4 :: c2:c3:c4:c5 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c2:c3:c4:c5 c5 :: c2:c3:c4:c5 A__PROD :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add -> c6:c7:c8:c9:c10 c6 :: c6:c7:c8:c9:c10 c7 :: c2:c3:c4:c5 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c6:c7:c8:c9:c10 a__prod :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add c8 :: c2:c3:c4:c5 -> c6:c7:c8:c9:c10 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c6:c7:c8:c9:c10 c9 :: c2:c3:c4:c5 -> c6:c7:c8:c9:c10 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c6:c7:c8:c9:c10 c10 :: c6:c7:c8:c9:c10 true :: 0':s:p:fact:prod:true:false:if:zero:add c11 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c11:c12:c13 false :: 0':s:p:fact:prod:true:false:if:zero:add c12 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c11:c12:c13 c13 :: c11:c12:c13 c14 :: c14:c15:c16 c15 :: c14:c15:c16 c16 :: c14:c15:c16 A__P :: 0':s:p:fact:prod:true:false:if:zero:add -> c17:c18 c17 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c17:c18 c18 :: c17:c18 c19 :: c:c1 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 if :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add c20 :: c11:c12:c13 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 zero :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add c21 :: c14:c15:c16 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 c22 :: c6:c7:c8:c9:c10 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 c23 :: c6:c7:c8:c9:c10 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 c24 :: c17:c18 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 add :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add c25 :: c2:c3:c4:c5 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 c26 :: c2:c3:c4:c5 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 c27 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 c28 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 c29 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 c30 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 a__fact :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add a__if :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add a__add :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add a__p :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add hole_c:c11_31 :: c:c1 hole_0':s:p:fact:prod:true:false:if:zero:add2_31 :: 0':s:p:fact:prod:true:false:if:zero:add hole_c11:c12:c133_31 :: c11:c12:c13 hole_c14:c15:c164_31 :: c14:c15:c16 hole_c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c305_31 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 hole_c2:c3:c4:c56_31 :: c2:c3:c4:c5 hole_c6:c7:c8:c9:c107_31 :: c6:c7:c8:c9:c10 hole_c17:c188_31 :: c17:c18 gen_0':s:p:fact:prod:true:false:if:zero:add9_31 :: Nat -> 0':s:p:fact:prod:true:false:if:zero:add gen_c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c3010_31 :: Nat -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 gen_c2:c3:c4:c511_31 :: Nat -> c2:c3:c4:c5 gen_c6:c7:c8:c9:c1012_31 :: Nat -> c6:c7:c8:c9:c10 Lemmas: mark(gen_0':s:p:fact:prod:true:false:if:zero:add9_31(n303395_31)) -> gen_0':s:p:fact:prod:true:false:if:zero:add9_31(n303395_31), rt in Omega(0) Generator Equations: gen_0':s:p:fact:prod:true:false:if:zero:add9_31(0) <=> 0' gen_0':s:p:fact:prod:true:false:if:zero:add9_31(+(x, 1)) <=> s(gen_0':s:p:fact:prod:true:false:if:zero:add9_31(x)) gen_c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c3010_31(0) <=> c28 gen_c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c3010_31(+(x, 1)) <=> c19(c(c11(c28), c14, c28), gen_c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c3010_31(x)) gen_c2:c3:c4:c511_31(0) <=> c2(c28) gen_c2:c3:c4:c511_31(+(x, 1)) <=> c3(gen_c2:c3:c4:c511_31(x), c28) gen_c6:c7:c8:c9:c1012_31(0) <=> c6 gen_c6:c7:c8:c9:c1012_31(+(x, 1)) <=> c8(c2(c28), gen_c6:c7:c8:c9:c1012_31(x), c28) The following defined symbols remain to be analysed: a__prod, A__FACT, A__IF, MARK, A__ADD, A__PROD, A__P, a__fact, a__if, a__add, a__p They will be analysed ascendingly in the following order: A__FACT = A__IF mark < A__FACT A__FACT = MARK A__FACT = A__ADD A__FACT = A__PROD A__FACT = A__P A__IF = MARK A__IF = A__ADD A__IF = A__PROD A__IF = A__P mark < MARK mark < A__ADD mark < A__PROD mark = a__prod mark = a__fact mark = a__if mark = a__add mark = a__p MARK = A__ADD MARK = A__PROD MARK = A__P A__ADD = A__PROD A__ADD = A__P a__prod < A__PROD A__PROD = A__P a__prod = a__fact a__prod = a__if a__prod = a__add a__prod = a__p a__fact = a__if a__fact = a__add a__fact = a__p a__if = a__add a__if = a__p a__add = a__p ---------------------------------------- (19) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: a__prod(gen_0':s:p:fact:prod:true:false:if:zero:add9_31(n307809_31), gen_0':s:p:fact:prod:true:false:if:zero:add9_31(0)) -> gen_0':s:p:fact:prod:true:false:if:zero:add9_31(0), rt in Omega(0) Induction Base: a__prod(gen_0':s:p:fact:prod:true:false:if:zero:add9_31(0), gen_0':s:p:fact:prod:true:false:if:zero:add9_31(0)) ->_R^Omega(0) 0' Induction Step: a__prod(gen_0':s:p:fact:prod:true:false:if:zero:add9_31(+(n307809_31, 1)), gen_0':s:p:fact:prod:true:false:if:zero:add9_31(0)) ->_R^Omega(0) a__add(mark(gen_0':s:p:fact:prod:true:false:if:zero:add9_31(0)), a__prod(mark(gen_0':s:p:fact:prod:true:false:if:zero:add9_31(n307809_31)), mark(gen_0':s:p:fact:prod:true:false:if:zero:add9_31(0)))) ->_L^Omega(0) a__add(gen_0':s:p:fact:prod:true:false:if:zero:add9_31(0), a__prod(mark(gen_0':s:p:fact:prod:true:false:if:zero:add9_31(n307809_31)), mark(gen_0':s:p:fact:prod:true:false:if:zero:add9_31(0)))) ->_L^Omega(0) a__add(gen_0':s:p:fact:prod:true:false:if:zero:add9_31(0), a__prod(gen_0':s:p:fact:prod:true:false:if:zero:add9_31(n307809_31), mark(gen_0':s:p:fact:prod:true:false:if:zero:add9_31(0)))) ->_L^Omega(0) a__add(gen_0':s:p:fact:prod:true:false:if:zero:add9_31(0), a__prod(gen_0':s:p:fact:prod:true:false:if:zero:add9_31(n307809_31), gen_0':s:p:fact:prod:true:false:if:zero:add9_31(0))) ->_IH a__add(gen_0':s:p:fact:prod:true:false:if:zero:add9_31(0), gen_0':s:p:fact:prod:true:false:if:zero:add9_31(0)) ->_R^Omega(0) mark(gen_0':s:p:fact:prod:true:false:if:zero:add9_31(0)) ->_L^Omega(0) gen_0':s:p:fact:prod:true:false:if:zero:add9_31(0) 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__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0'), prod(z0, fact(p(z0)))), A__ZERO(mark(z0)), MARK(z0)) A__FACT(z0) -> c1 A__ADD(0', z0) -> c2(MARK(z0)) A__ADD(s(z0), z1) -> c3(A__ADD(mark(z0), mark(z1)), MARK(z0)) A__ADD(s(z0), z1) -> c4(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__ADD(z0, z1) -> c5 A__PROD(0', z0) -> c6 A__PROD(s(z0), z1) -> c7(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), MARK(z1)) A__PROD(s(z0), z1) -> c8(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z0)) A__PROD(s(z0), z1) -> c9(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z1)) A__PROD(z0, z1) -> c10 A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__IF(z0, z1, z2) -> c13 A__ZERO(0') -> c14 A__ZERO(s(z0)) -> c15 A__ZERO(z0) -> c16 A__P(s(z0)) -> c17(MARK(z0)) A__P(z0) -> c18 MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(if(z0, z1, z2)) -> c20(A__IF(mark(z0), z1, z2), MARK(z0)) MARK(zero(z0)) -> c21(A__ZERO(mark(z0)), MARK(z0)) MARK(prod(z0, z1)) -> c22(A__PROD(mark(z0), mark(z1)), MARK(z0)) MARK(prod(z0, z1)) -> c23(A__PROD(mark(z0), mark(z1)), MARK(z1)) MARK(p(z0)) -> c24(A__P(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) MARK(0') -> c28 MARK(true) -> c29 MARK(false) -> c30 a__fact(z0) -> a__if(a__zero(mark(z0)), s(0'), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0', z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0', z0) -> 0' a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0') -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0') -> 0' mark(true) -> true mark(false) -> false Types: A__FACT :: 0':s:p:fact:prod:true:false:if:zero:add -> c:c1 c :: c11:c12:c13 -> c14:c15:c16 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c:c1 A__IF :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add -> c11:c12:c13 a__zero :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add mark :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add s :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add 0' :: 0':s:p:fact:prod:true:false:if:zero:add prod :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add fact :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add p :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add A__ZERO :: 0':s:p:fact:prod:true:false:if:zero:add -> c14:c15:c16 MARK :: 0':s:p:fact:prod:true:false:if:zero:add -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 c1 :: c:c1 A__ADD :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add -> c2:c3:c4:c5 c2 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c2:c3:c4:c5 c3 :: c2:c3:c4:c5 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c2:c3:c4:c5 c4 :: c2:c3:c4:c5 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c2:c3:c4:c5 c5 :: c2:c3:c4:c5 A__PROD :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add -> c6:c7:c8:c9:c10 c6 :: c6:c7:c8:c9:c10 c7 :: c2:c3:c4:c5 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c6:c7:c8:c9:c10 a__prod :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add c8 :: c2:c3:c4:c5 -> c6:c7:c8:c9:c10 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c6:c7:c8:c9:c10 c9 :: c2:c3:c4:c5 -> c6:c7:c8:c9:c10 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c6:c7:c8:c9:c10 c10 :: c6:c7:c8:c9:c10 true :: 0':s:p:fact:prod:true:false:if:zero:add c11 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c11:c12:c13 false :: 0':s:p:fact:prod:true:false:if:zero:add c12 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c11:c12:c13 c13 :: c11:c12:c13 c14 :: c14:c15:c16 c15 :: c14:c15:c16 c16 :: c14:c15:c16 A__P :: 0':s:p:fact:prod:true:false:if:zero:add -> c17:c18 c17 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c17:c18 c18 :: c17:c18 c19 :: c:c1 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 if :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add c20 :: c11:c12:c13 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 zero :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add c21 :: c14:c15:c16 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 c22 :: c6:c7:c8:c9:c10 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 c23 :: c6:c7:c8:c9:c10 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 c24 :: c17:c18 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 add :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add c25 :: c2:c3:c4:c5 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 c26 :: c2:c3:c4:c5 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 c27 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 c28 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 c29 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 c30 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 a__fact :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add a__if :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add a__add :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add a__p :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add hole_c:c11_31 :: c:c1 hole_0':s:p:fact:prod:true:false:if:zero:add2_31 :: 0':s:p:fact:prod:true:false:if:zero:add hole_c11:c12:c133_31 :: c11:c12:c13 hole_c14:c15:c164_31 :: c14:c15:c16 hole_c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c305_31 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 hole_c2:c3:c4:c56_31 :: c2:c3:c4:c5 hole_c6:c7:c8:c9:c107_31 :: c6:c7:c8:c9:c10 hole_c17:c188_31 :: c17:c18 gen_0':s:p:fact:prod:true:false:if:zero:add9_31 :: Nat -> 0':s:p:fact:prod:true:false:if:zero:add gen_c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c3010_31 :: Nat -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 gen_c2:c3:c4:c511_31 :: Nat -> c2:c3:c4:c5 gen_c6:c7:c8:c9:c1012_31 :: Nat -> c6:c7:c8:c9:c10 Lemmas: mark(gen_0':s:p:fact:prod:true:false:if:zero:add9_31(n303395_31)) -> gen_0':s:p:fact:prod:true:false:if:zero:add9_31(n303395_31), rt in Omega(0) a__prod(gen_0':s:p:fact:prod:true:false:if:zero:add9_31(n307809_31), gen_0':s:p:fact:prod:true:false:if:zero:add9_31(0)) -> gen_0':s:p:fact:prod:true:false:if:zero:add9_31(0), rt in Omega(0) Generator Equations: gen_0':s:p:fact:prod:true:false:if:zero:add9_31(0) <=> 0' gen_0':s:p:fact:prod:true:false:if:zero:add9_31(+(x, 1)) <=> s(gen_0':s:p:fact:prod:true:false:if:zero:add9_31(x)) gen_c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c3010_31(0) <=> c28 gen_c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c3010_31(+(x, 1)) <=> c19(c(c11(c28), c14, c28), gen_c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c3010_31(x)) gen_c2:c3:c4:c511_31(0) <=> c2(c28) gen_c2:c3:c4:c511_31(+(x, 1)) <=> c3(gen_c2:c3:c4:c511_31(x), c28) gen_c6:c7:c8:c9:c1012_31(0) <=> c6 gen_c6:c7:c8:c9:c1012_31(+(x, 1)) <=> c8(c2(c28), gen_c6:c7:c8:c9:c1012_31(x), c28) The following defined symbols remain to be analysed: a__add, A__FACT, A__IF, mark, MARK, A__ADD, A__PROD, A__P, a__fact, a__if, a__p They will be analysed ascendingly in the following order: A__FACT = A__IF mark < A__FACT A__FACT = MARK A__FACT = A__ADD A__FACT = A__PROD A__FACT = A__P A__IF = MARK A__IF = A__ADD A__IF = A__PROD A__IF = A__P mark < MARK mark < A__ADD mark < A__PROD mark = a__prod mark = a__fact mark = a__if mark = a__add mark = a__p MARK = A__ADD MARK = A__PROD MARK = A__P A__ADD = A__PROD A__ADD = A__P a__prod < A__PROD A__PROD = A__P a__prod = a__fact a__prod = a__if a__prod = a__add a__prod = a__p a__fact = a__if a__fact = a__add a__fact = a__p a__if = a__add a__if = a__p a__add = a__p ---------------------------------------- (21) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: a__add(gen_0':s:p:fact:prod:true:false:if:zero:add9_31(n324164_31), gen_0':s:p:fact:prod:true:false:if:zero:add9_31(b)) -> gen_0':s:p:fact:prod:true:false:if:zero:add9_31(+(n324164_31, b)), rt in Omega(0) Induction Base: a__add(gen_0':s:p:fact:prod:true:false:if:zero:add9_31(0), gen_0':s:p:fact:prod:true:false:if:zero:add9_31(b)) ->_R^Omega(0) mark(gen_0':s:p:fact:prod:true:false:if:zero:add9_31(b)) ->_L^Omega(0) gen_0':s:p:fact:prod:true:false:if:zero:add9_31(b) Induction Step: a__add(gen_0':s:p:fact:prod:true:false:if:zero:add9_31(+(n324164_31, 1)), gen_0':s:p:fact:prod:true:false:if:zero:add9_31(b)) ->_R^Omega(0) s(a__add(mark(gen_0':s:p:fact:prod:true:false:if:zero:add9_31(n324164_31)), mark(gen_0':s:p:fact:prod:true:false:if:zero:add9_31(b)))) ->_L^Omega(0) s(a__add(gen_0':s:p:fact:prod:true:false:if:zero:add9_31(n324164_31), mark(gen_0':s:p:fact:prod:true:false:if:zero:add9_31(b)))) ->_L^Omega(0) s(a__add(gen_0':s:p:fact:prod:true:false:if:zero:add9_31(n324164_31), gen_0':s:p:fact:prod:true:false:if:zero:add9_31(b))) ->_IH s(gen_0':s:p:fact:prod:true:false:if:zero:add9_31(+(b, c324165_31))) 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__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0'), prod(z0, fact(p(z0)))), A__ZERO(mark(z0)), MARK(z0)) A__FACT(z0) -> c1 A__ADD(0', z0) -> c2(MARK(z0)) A__ADD(s(z0), z1) -> c3(A__ADD(mark(z0), mark(z1)), MARK(z0)) A__ADD(s(z0), z1) -> c4(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__ADD(z0, z1) -> c5 A__PROD(0', z0) -> c6 A__PROD(s(z0), z1) -> c7(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), MARK(z1)) A__PROD(s(z0), z1) -> c8(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z0)) A__PROD(s(z0), z1) -> c9(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z1)) A__PROD(z0, z1) -> c10 A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__IF(z0, z1, z2) -> c13 A__ZERO(0') -> c14 A__ZERO(s(z0)) -> c15 A__ZERO(z0) -> c16 A__P(s(z0)) -> c17(MARK(z0)) A__P(z0) -> c18 MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(if(z0, z1, z2)) -> c20(A__IF(mark(z0), z1, z2), MARK(z0)) MARK(zero(z0)) -> c21(A__ZERO(mark(z0)), MARK(z0)) MARK(prod(z0, z1)) -> c22(A__PROD(mark(z0), mark(z1)), MARK(z0)) MARK(prod(z0, z1)) -> c23(A__PROD(mark(z0), mark(z1)), MARK(z1)) MARK(p(z0)) -> c24(A__P(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) MARK(0') -> c28 MARK(true) -> c29 MARK(false) -> c30 a__fact(z0) -> a__if(a__zero(mark(z0)), s(0'), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0', z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0', z0) -> 0' a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0') -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0') -> 0' mark(true) -> true mark(false) -> false Types: A__FACT :: 0':s:p:fact:prod:true:false:if:zero:add -> c:c1 c :: c11:c12:c13 -> c14:c15:c16 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c:c1 A__IF :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add -> c11:c12:c13 a__zero :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add mark :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add s :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add 0' :: 0':s:p:fact:prod:true:false:if:zero:add prod :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add fact :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add p :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add A__ZERO :: 0':s:p:fact:prod:true:false:if:zero:add -> c14:c15:c16 MARK :: 0':s:p:fact:prod:true:false:if:zero:add -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 c1 :: c:c1 A__ADD :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add -> c2:c3:c4:c5 c2 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c2:c3:c4:c5 c3 :: c2:c3:c4:c5 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c2:c3:c4:c5 c4 :: c2:c3:c4:c5 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c2:c3:c4:c5 c5 :: c2:c3:c4:c5 A__PROD :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add -> c6:c7:c8:c9:c10 c6 :: c6:c7:c8:c9:c10 c7 :: c2:c3:c4:c5 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c6:c7:c8:c9:c10 a__prod :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add c8 :: c2:c3:c4:c5 -> c6:c7:c8:c9:c10 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c6:c7:c8:c9:c10 c9 :: c2:c3:c4:c5 -> c6:c7:c8:c9:c10 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c6:c7:c8:c9:c10 c10 :: c6:c7:c8:c9:c10 true :: 0':s:p:fact:prod:true:false:if:zero:add c11 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c11:c12:c13 false :: 0':s:p:fact:prod:true:false:if:zero:add c12 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c11:c12:c13 c13 :: c11:c12:c13 c14 :: c14:c15:c16 c15 :: c14:c15:c16 c16 :: c14:c15:c16 A__P :: 0':s:p:fact:prod:true:false:if:zero:add -> c17:c18 c17 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c17:c18 c18 :: c17:c18 c19 :: c:c1 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 if :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add c20 :: c11:c12:c13 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 zero :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add c21 :: c14:c15:c16 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 c22 :: c6:c7:c8:c9:c10 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 c23 :: c6:c7:c8:c9:c10 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 c24 :: c17:c18 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 add :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add c25 :: c2:c3:c4:c5 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 c26 :: c2:c3:c4:c5 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 c27 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 c28 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 c29 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 c30 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 a__fact :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add a__if :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add a__add :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add a__p :: 0':s:p:fact:prod:true:false:if:zero:add -> 0':s:p:fact:prod:true:false:if:zero:add hole_c:c11_31 :: c:c1 hole_0':s:p:fact:prod:true:false:if:zero:add2_31 :: 0':s:p:fact:prod:true:false:if:zero:add hole_c11:c12:c133_31 :: c11:c12:c13 hole_c14:c15:c164_31 :: c14:c15:c16 hole_c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c305_31 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 hole_c2:c3:c4:c56_31 :: c2:c3:c4:c5 hole_c6:c7:c8:c9:c107_31 :: c6:c7:c8:c9:c10 hole_c17:c188_31 :: c17:c18 gen_0':s:p:fact:prod:true:false:if:zero:add9_31 :: Nat -> 0':s:p:fact:prod:true:false:if:zero:add gen_c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c3010_31 :: Nat -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30 gen_c2:c3:c4:c511_31 :: Nat -> c2:c3:c4:c5 gen_c6:c7:c8:c9:c1012_31 :: Nat -> c6:c7:c8:c9:c10 Lemmas: mark(gen_0':s:p:fact:prod:true:false:if:zero:add9_31(n303395_31)) -> gen_0':s:p:fact:prod:true:false:if:zero:add9_31(n303395_31), rt in Omega(0) a__prod(gen_0':s:p:fact:prod:true:false:if:zero:add9_31(n307809_31), gen_0':s:p:fact:prod:true:false:if:zero:add9_31(0)) -> gen_0':s:p:fact:prod:true:false:if:zero:add9_31(0), rt in Omega(0) a__add(gen_0':s:p:fact:prod:true:false:if:zero:add9_31(n324164_31), gen_0':s:p:fact:prod:true:false:if:zero:add9_31(b)) -> gen_0':s:p:fact:prod:true:false:if:zero:add9_31(+(n324164_31, b)), rt in Omega(0) Generator Equations: gen_0':s:p:fact:prod:true:false:if:zero:add9_31(0) <=> 0' gen_0':s:p:fact:prod:true:false:if:zero:add9_31(+(x, 1)) <=> s(gen_0':s:p:fact:prod:true:false:if:zero:add9_31(x)) gen_c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c3010_31(0) <=> c28 gen_c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c3010_31(+(x, 1)) <=> c19(c(c11(c28), c14, c28), gen_c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c3010_31(x)) gen_c2:c3:c4:c511_31(0) <=> c2(c28) gen_c2:c3:c4:c511_31(+(x, 1)) <=> c3(gen_c2:c3:c4:c511_31(x), c28) gen_c6:c7:c8:c9:c1012_31(0) <=> c6 gen_c6:c7:c8:c9:c1012_31(+(x, 1)) <=> c8(c2(c28), gen_c6:c7:c8:c9:c1012_31(x), c28) The following defined symbols remain to be analysed: a__p, A__FACT, A__IF, mark, MARK, A__ADD, A__PROD, a__prod, A__P, a__fact, a__if They will be analysed ascendingly in the following order: A__FACT = A__IF mark < A__FACT A__FACT = MARK A__FACT = A__ADD A__FACT = A__PROD A__FACT = A__P A__IF = MARK A__IF = A__ADD A__IF = A__PROD A__IF = A__P mark < MARK mark < A__ADD mark < A__PROD mark = a__prod mark = a__fact mark = a__if mark = a__add mark = a__p MARK = A__ADD MARK = A__PROD MARK = A__P A__ADD = A__PROD A__ADD = A__P a__prod < A__PROD A__PROD = A__P a__prod = a__fact a__prod = a__if a__prod = a__add a__prod = a__p a__fact = a__if a__fact = a__add a__fact = a__p a__if = a__add a__if = a__p a__add = a__p ---------------------------------------- (23) RelTrsToWeightedTrsProof (UPPER BOUND(ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (24) 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__fact(X) -> a__if(a__zero(mark(X)), s(0), prod(X, fact(p(X)))) [1] a__add(0, X) -> mark(X) [1] a__add(s(X), Y) -> s(a__add(mark(X), mark(Y))) [1] a__prod(0, X) -> 0 [1] a__prod(s(X), Y) -> a__add(mark(Y), a__prod(mark(X), mark(Y))) [1] a__if(true, X, Y) -> mark(X) [1] a__if(false, X, Y) -> mark(Y) [1] a__zero(0) -> true [1] a__zero(s(X)) -> false [1] a__p(s(X)) -> mark(X) [1] mark(fact(X)) -> a__fact(mark(X)) [1] mark(if(X1, X2, X3)) -> a__if(mark(X1), X2, X3) [1] mark(zero(X)) -> a__zero(mark(X)) [1] mark(prod(X1, X2)) -> a__prod(mark(X1), mark(X2)) [1] mark(p(X)) -> a__p(mark(X)) [1] mark(add(X1, X2)) -> a__add(mark(X1), mark(X2)) [1] mark(s(X)) -> s(mark(X)) [1] mark(0) -> 0 [1] mark(true) -> true [1] mark(false) -> false [1] a__fact(X) -> fact(X) [1] a__if(X1, X2, X3) -> if(X1, X2, X3) [1] a__zero(X) -> zero(X) [1] a__prod(X1, X2) -> prod(X1, X2) [1] a__p(X) -> p(X) [1] a__add(X1, X2) -> add(X1, X2) [1] Rewrite Strategy: INNERMOST ---------------------------------------- (25) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (26) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__fact(X) -> a__if(a__zero(mark(X)), s(0), prod(X, fact(p(X)))) [1] a__add(0, X) -> mark(X) [1] a__add(s(X), Y) -> s(a__add(mark(X), mark(Y))) [1] a__prod(0, X) -> 0 [1] a__prod(s(X), Y) -> a__add(mark(Y), a__prod(mark(X), mark(Y))) [1] a__if(true, X, Y) -> mark(X) [1] a__if(false, X, Y) -> mark(Y) [1] a__zero(0) -> true [1] a__zero(s(X)) -> false [1] a__p(s(X)) -> mark(X) [1] mark(fact(X)) -> a__fact(mark(X)) [1] mark(if(X1, X2, X3)) -> a__if(mark(X1), X2, X3) [1] mark(zero(X)) -> a__zero(mark(X)) [1] mark(prod(X1, X2)) -> a__prod(mark(X1), mark(X2)) [1] mark(p(X)) -> a__p(mark(X)) [1] mark(add(X1, X2)) -> a__add(mark(X1), mark(X2)) [1] mark(s(X)) -> s(mark(X)) [1] mark(0) -> 0 [1] mark(true) -> true [1] mark(false) -> false [1] a__fact(X) -> fact(X) [1] a__if(X1, X2, X3) -> if(X1, X2, X3) [1] a__zero(X) -> zero(X) [1] a__prod(X1, X2) -> prod(X1, X2) [1] a__p(X) -> p(X) [1] a__add(X1, X2) -> add(X1, X2) [1] The TRS has the following type information: a__fact :: 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add a__if :: 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add a__zero :: 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add mark :: 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add s :: 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add 0 :: 0:s:p:fact:prod:true:false:if:zero:add prod :: 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add fact :: 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add p :: 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add a__add :: 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add a__prod :: 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add true :: 0:s:p:fact:prod:true:false:if:zero:add false :: 0:s:p:fact:prod:true:false:if:zero:add a__p :: 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add if :: 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add zero :: 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add add :: 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add Rewrite Strategy: INNERMOST ---------------------------------------- (27) 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 ---------------------------------------- (28) 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__fact(X) -> a__if(a__zero(mark(X)), s(0), prod(X, fact(p(X)))) [1] a__add(0, X) -> mark(X) [1] a__add(s(X), Y) -> s(a__add(mark(X), mark(Y))) [1] a__prod(0, X) -> 0 [1] a__prod(s(X), Y) -> a__add(mark(Y), a__prod(mark(X), mark(Y))) [1] a__if(true, X, Y) -> mark(X) [1] a__if(false, X, Y) -> mark(Y) [1] a__zero(0) -> true [1] a__zero(s(X)) -> false [1] a__p(s(X)) -> mark(X) [1] mark(fact(X)) -> a__fact(mark(X)) [1] mark(if(X1, X2, X3)) -> a__if(mark(X1), X2, X3) [1] mark(zero(X)) -> a__zero(mark(X)) [1] mark(prod(X1, X2)) -> a__prod(mark(X1), mark(X2)) [1] mark(p(X)) -> a__p(mark(X)) [1] mark(add(X1, X2)) -> a__add(mark(X1), mark(X2)) [1] mark(s(X)) -> s(mark(X)) [1] mark(0) -> 0 [1] mark(true) -> true [1] mark(false) -> false [1] a__fact(X) -> fact(X) [1] a__if(X1, X2, X3) -> if(X1, X2, X3) [1] a__zero(X) -> zero(X) [1] a__prod(X1, X2) -> prod(X1, X2) [1] a__p(X) -> p(X) [1] a__add(X1, X2) -> add(X1, X2) [1] The TRS has the following type information: a__fact :: 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add a__if :: 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add a__zero :: 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add mark :: 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add s :: 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add 0 :: 0:s:p:fact:prod:true:false:if:zero:add prod :: 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add fact :: 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add p :: 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add a__add :: 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add a__prod :: 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add true :: 0:s:p:fact:prod:true:false:if:zero:add false :: 0:s:p:fact:prod:true:false:if:zero:add a__p :: 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add if :: 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add zero :: 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add add :: 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add Rewrite Strategy: INNERMOST ---------------------------------------- (29) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: 0 => 0 true => 2 false => 1 ---------------------------------------- (30) Obligation: Complexity RNTS consisting of the following rules: a__add(z, z') -{ 1 }-> mark(X) :|: z' = X, X >= 0, z = 0 a__add(z, z') -{ 1 }-> 1 + a__add(mark(X), mark(Y)) :|: z = 1 + X, z' = Y, Y >= 0, X >= 0 a__add(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__fact(z) -{ 1 }-> a__if(a__zero(mark(X)), 1 + 0, 1 + X + (1 + (1 + X))) :|: X >= 0, z = X a__fact(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__if(z, z', z'') -{ 1 }-> mark(X) :|: z = 2, z' = X, Y >= 0, z'' = Y, X >= 0 a__if(z, z', z'') -{ 1 }-> mark(Y) :|: z' = X, Y >= 0, z = 1, z'' = Y, X >= 0 a__if(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__p(z) -{ 1 }-> mark(X) :|: z = 1 + X, X >= 0 a__p(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__prod(z, z') -{ 1 }-> a__add(mark(Y), a__prod(mark(X), mark(Y))) :|: z = 1 + X, z' = Y, Y >= 0, X >= 0 a__prod(z, z') -{ 1 }-> 0 :|: z' = X, X >= 0, z = 0 a__prod(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__zero(z) -{ 1 }-> 2 :|: z = 0 a__zero(z) -{ 1 }-> 1 :|: z = 1 + X, X >= 0 a__zero(z) -{ 1 }-> 1 + X :|: X >= 0, z = X mark(z) -{ 1 }-> a__zero(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__prod(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__p(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__if(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> a__fact(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__add(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> 2 :|: z = 2 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. ---------------------------------------- (31) 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: a__zero_1 mark_1 a__prod_2 a__fact_1 a__if_3 a__p_1 a__add_2 Due to the following rules being added: none And the following fresh constants: none ---------------------------------------- (32) 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__fact(X) -> a__if(a__zero(mark(X)), s(0), prod(X, fact(p(X)))) [1] a__add(0, X) -> mark(X) [1] a__add(s(X), Y) -> s(a__add(mark(X), mark(Y))) [1] a__prod(0, X) -> 0 [1] a__prod(s(X), Y) -> a__add(mark(Y), a__prod(mark(X), mark(Y))) [1] a__if(true, X, Y) -> mark(X) [1] a__if(false, X, Y) -> mark(Y) [1] a__zero(0) -> true [1] a__zero(s(X)) -> false [1] a__p(s(X)) -> mark(X) [1] mark(fact(X)) -> a__fact(mark(X)) [1] mark(if(X1, X2, X3)) -> a__if(mark(X1), X2, X3) [1] mark(zero(X)) -> a__zero(mark(X)) [1] mark(prod(X1, X2)) -> a__prod(mark(X1), mark(X2)) [1] mark(p(X)) -> a__p(mark(X)) [1] mark(add(X1, X2)) -> a__add(mark(X1), mark(X2)) [1] mark(s(X)) -> s(mark(X)) [1] mark(0) -> 0 [1] mark(true) -> true [1] mark(false) -> false [1] a__fact(X) -> fact(X) [1] a__if(X1, X2, X3) -> if(X1, X2, X3) [1] a__zero(X) -> zero(X) [1] a__prod(X1, X2) -> prod(X1, X2) [1] a__p(X) -> p(X) [1] a__add(X1, X2) -> add(X1, X2) [1] The TRS has the following type information: a__fact :: 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add a__if :: 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add a__zero :: 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add mark :: 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add s :: 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add 0 :: 0:s:p:fact:prod:true:false:if:zero:add prod :: 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add fact :: 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add p :: 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add a__add :: 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add a__prod :: 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add true :: 0:s:p:fact:prod:true:false:if:zero:add false :: 0:s:p:fact:prod:true:false:if:zero:add a__p :: 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add if :: 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add zero :: 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add add :: 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add Rewrite Strategy: INNERMOST ---------------------------------------- (33) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (34) 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__fact(fact(X')) -> a__if(a__zero(a__fact(mark(X'))), s(0), prod(fact(X'), fact(p(fact(X'))))) [2] a__fact(if(X1', X2', X3')) -> a__if(a__zero(a__if(mark(X1'), X2', X3')), s(0), prod(if(X1', X2', X3'), fact(p(if(X1', X2', X3'))))) [2] a__fact(zero(X'')) -> a__if(a__zero(a__zero(mark(X''))), s(0), prod(zero(X''), fact(p(zero(X''))))) [2] a__fact(prod(X1'', X2'')) -> a__if(a__zero(a__prod(mark(X1''), mark(X2''))), s(0), prod(prod(X1'', X2''), fact(p(prod(X1'', X2''))))) [2] a__fact(p(X4)) -> a__if(a__zero(a__p(mark(X4))), s(0), prod(p(X4), fact(p(p(X4))))) [2] a__fact(add(X11, X21)) -> a__if(a__zero(a__add(mark(X11), mark(X21))), s(0), prod(add(X11, X21), fact(p(add(X11, X21))))) [2] a__fact(s(X5)) -> a__if(a__zero(s(mark(X5))), s(0), prod(s(X5), fact(p(s(X5))))) [2] a__fact(0) -> a__if(a__zero(0), s(0), prod(0, fact(p(0)))) [2] a__fact(true) -> a__if(a__zero(true), s(0), prod(true, fact(p(true)))) [2] a__fact(false) -> a__if(a__zero(false), s(0), prod(false, fact(p(false)))) [2] a__add(0, X) -> mark(X) [1] a__add(s(X), Y) -> s(a__add(mark(X), mark(Y))) [1] a__prod(0, X) -> 0 [1] a__prod(s(X), Y) -> a__add(mark(Y), a__prod(mark(X), mark(Y))) [1] a__if(true, X, Y) -> mark(X) [1] a__if(false, X, Y) -> mark(Y) [1] a__zero(0) -> true [1] a__zero(s(X)) -> false [1] a__p(s(X)) -> mark(X) [1] mark(fact(fact(X172))) -> a__fact(a__fact(mark(X172))) [2] mark(fact(if(X173, X269, X328))) -> a__fact(a__if(mark(X173), X269, X328)) [2] mark(fact(zero(X174))) -> a__fact(a__zero(mark(X174))) [2] mark(fact(prod(X175, X270))) -> a__fact(a__prod(mark(X175), mark(X270))) [2] mark(fact(p(X176))) -> a__fact(a__p(mark(X176))) [2] mark(fact(add(X177, X271))) -> a__fact(a__add(mark(X177), mark(X271))) [2] mark(fact(s(X178))) -> a__fact(s(mark(X178))) [2] mark(fact(0)) -> a__fact(0) [2] mark(fact(true)) -> a__fact(true) [2] mark(fact(false)) -> a__fact(false) [2] mark(if(fact(X179), X2, X3)) -> a__if(a__fact(mark(X179)), X2, X3) [2] mark(if(if(X180, X272, X329), X2, X3)) -> a__if(a__if(mark(X180), X272, X329), X2, X3) [2] mark(if(zero(X181), X2, X3)) -> a__if(a__zero(mark(X181)), X2, X3) [2] mark(if(prod(X182, X273), X2, X3)) -> a__if(a__prod(mark(X182), mark(X273)), X2, X3) [2] mark(if(p(X183), X2, X3)) -> a__if(a__p(mark(X183)), X2, X3) [2] mark(if(add(X184, X274), X2, X3)) -> a__if(a__add(mark(X184), mark(X274)), X2, X3) [2] mark(if(s(X185), X2, X3)) -> a__if(s(mark(X185)), X2, X3) [2] mark(if(0, X2, X3)) -> a__if(0, X2, X3) [2] mark(if(true, X2, X3)) -> a__if(true, X2, X3) [2] mark(if(false, X2, X3)) -> a__if(false, X2, X3) [2] mark(zero(fact(X186))) -> a__zero(a__fact(mark(X186))) [2] mark(zero(if(X187, X275, X330))) -> a__zero(a__if(mark(X187), X275, X330)) [2] mark(zero(zero(X188))) -> a__zero(a__zero(mark(X188))) [2] mark(zero(prod(X189, X276))) -> a__zero(a__prod(mark(X189), mark(X276))) [2] mark(zero(p(X190))) -> a__zero(a__p(mark(X190))) [2] mark(zero(add(X191, X277))) -> a__zero(a__add(mark(X191), mark(X277))) [2] mark(zero(s(X192))) -> a__zero(s(mark(X192))) [2] mark(zero(0)) -> a__zero(0) [2] mark(zero(true)) -> a__zero(true) [2] mark(zero(false)) -> a__zero(false) [2] mark(prod(X1, X2)) -> a__prod(mark(X1), mark(X2)) [1] mark(p(fact(X355))) -> a__p(a__fact(mark(X355))) [2] mark(p(if(X1130, X2118, X356))) -> a__p(a__if(mark(X1130), X2118, X356)) [2] mark(p(zero(X357))) -> a__p(a__zero(mark(X357))) [2] mark(p(prod(X1131, X2119))) -> a__p(a__prod(mark(X1131), mark(X2119))) [2] mark(p(p(X358))) -> a__p(a__p(mark(X358))) [2] mark(p(add(X1132, X2120))) -> a__p(a__add(mark(X1132), mark(X2120))) [2] mark(p(s(X359))) -> a__p(s(mark(X359))) [2] mark(p(0)) -> a__p(0) [2] mark(p(true)) -> a__p(true) [2] mark(p(false)) -> a__p(false) [2] mark(add(X1, X2)) -> a__add(mark(X1), mark(X2)) [1] mark(s(X)) -> s(mark(X)) [1] mark(0) -> 0 [1] mark(true) -> true [1] mark(false) -> false [1] a__fact(X) -> fact(X) [1] a__if(X1, X2, X3) -> if(X1, X2, X3) [1] a__zero(X) -> zero(X) [1] a__prod(X1, X2) -> prod(X1, X2) [1] a__p(X) -> p(X) [1] a__add(X1, X2) -> add(X1, X2) [1] The TRS has the following type information: a__fact :: 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add a__if :: 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add a__zero :: 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add mark :: 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add s :: 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add 0 :: 0:s:p:fact:prod:true:false:if:zero:add prod :: 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add fact :: 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add p :: 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add a__add :: 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add a__prod :: 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add true :: 0:s:p:fact:prod:true:false:if:zero:add false :: 0:s:p:fact:prod:true:false:if:zero:add a__p :: 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add if :: 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add zero :: 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add add :: 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add -> 0:s:p:fact:prod:true:false:if:zero:add Rewrite Strategy: INNERMOST ---------------------------------------- (35) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: 0 => 0 true => 2 false => 1 ---------------------------------------- (36) Obligation: Complexity RNTS consisting of the following rules: a__add(z, z') -{ 1 }-> mark(X) :|: z' = X, X >= 0, z = 0 a__add(z, z') -{ 1 }-> 1 + a__add(mark(X), mark(Y)) :|: z = 1 + X, z' = Y, Y >= 0, X >= 0 a__add(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__fact(z) -{ 2 }-> a__if(a__zero(a__zero(mark(X''))), 1 + 0, 1 + (1 + X'') + (1 + (1 + (1 + X'')))) :|: z = 1 + X'', X'' >= 0 a__fact(z) -{ 2 }-> a__if(a__zero(a__prod(mark(X1''), mark(X2''))), 1 + 0, 1 + (1 + X1'' + X2'') + (1 + (1 + (1 + X1'' + X2'')))) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0 a__fact(z) -{ 2 }-> a__if(a__zero(a__p(mark(X4))), 1 + 0, 1 + (1 + X4) + (1 + (1 + (1 + X4)))) :|: z = 1 + X4, X4 >= 0 a__fact(z) -{ 2 }-> a__if(a__zero(a__if(mark(X1'), X2', X3')), 1 + 0, 1 + (1 + X1' + X2' + X3') + (1 + (1 + (1 + X1' + X2' + X3')))) :|: X3' >= 0, X2' >= 0, z = 1 + X1' + X2' + X3', X1' >= 0 a__fact(z) -{ 2 }-> a__if(a__zero(a__fact(mark(X'))), 1 + 0, 1 + (1 + X') + (1 + (1 + (1 + X')))) :|: X' >= 0, z = 1 + X' a__fact(z) -{ 2 }-> a__if(a__zero(a__add(mark(X11), mark(X21))), 1 + 0, 1 + (1 + X11 + X21) + (1 + (1 + (1 + X11 + X21)))) :|: X11 >= 0, X21 >= 0, z = 1 + X11 + X21 a__fact(z) -{ 2 }-> a__if(a__zero(2), 1 + 0, 1 + 2 + (1 + (1 + 2))) :|: z = 2 a__fact(z) -{ 2 }-> a__if(a__zero(1), 1 + 0, 1 + 1 + (1 + (1 + 1))) :|: z = 1 a__fact(z) -{ 2 }-> a__if(a__zero(0), 1 + 0, 1 + 0 + (1 + (1 + 0))) :|: z = 0 a__fact(z) -{ 2 }-> a__if(a__zero(1 + mark(X5)), 1 + 0, 1 + (1 + X5) + (1 + (1 + (1 + X5)))) :|: X5 >= 0, z = 1 + X5 a__fact(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__if(z, z', z'') -{ 1 }-> mark(X) :|: z = 2, z' = X, Y >= 0, z'' = Y, X >= 0 a__if(z, z', z'') -{ 1 }-> mark(Y) :|: z' = X, Y >= 0, z = 1, z'' = Y, X >= 0 a__if(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__p(z) -{ 1 }-> mark(X) :|: z = 1 + X, X >= 0 a__p(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__prod(z, z') -{ 1 }-> a__add(mark(Y), a__prod(mark(X), mark(Y))) :|: z = 1 + X, z' = Y, Y >= 0, X >= 0 a__prod(z, z') -{ 1 }-> 0 :|: z' = X, X >= 0, z = 0 a__prod(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__zero(z) -{ 1 }-> 2 :|: z = 0 a__zero(z) -{ 1 }-> 1 :|: z = 1 + X, X >= 0 a__zero(z) -{ 1 }-> 1 + X :|: X >= 0, z = X mark(z) -{ 2 }-> a__zero(a__zero(mark(X188))) :|: X188 >= 0, z = 1 + (1 + X188) mark(z) -{ 2 }-> a__zero(a__prod(mark(X189), mark(X276))) :|: X276 >= 0, z = 1 + (1 + X189 + X276), X189 >= 0 mark(z) -{ 2 }-> a__zero(a__p(mark(X190))) :|: z = 1 + (1 + X190), X190 >= 0 mark(z) -{ 2 }-> a__zero(a__if(mark(X187), X275, X330)) :|: X187 >= 0, X275 >= 0, z = 1 + (1 + X187 + X275 + X330), X330 >= 0 mark(z) -{ 2 }-> a__zero(a__fact(mark(X186))) :|: z = 1 + (1 + X186), X186 >= 0 mark(z) -{ 2 }-> a__zero(a__add(mark(X191), mark(X277))) :|: z = 1 + (1 + X191 + X277), X191 >= 0, X277 >= 0 mark(z) -{ 2 }-> a__zero(2) :|: z = 1 + 2 mark(z) -{ 2 }-> a__zero(1) :|: z = 1 + 1 mark(z) -{ 2 }-> a__zero(0) :|: z = 1 + 0 mark(z) -{ 2 }-> a__zero(1 + mark(X192)) :|: X192 >= 0, z = 1 + (1 + X192) mark(z) -{ 1 }-> a__prod(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 2 }-> a__p(a__zero(mark(X357))) :|: z = 1 + (1 + X357), X357 >= 0 mark(z) -{ 2 }-> a__p(a__prod(mark(X1131), mark(X2119))) :|: z = 1 + (1 + X1131 + X2119), X2119 >= 0, X1131 >= 0 mark(z) -{ 2 }-> a__p(a__p(mark(X358))) :|: X358 >= 0, z = 1 + (1 + X358) mark(z) -{ 2 }-> a__p(a__if(mark(X1130), X2118, X356)) :|: X2118 >= 0, X1130 >= 0, z = 1 + (1 + X1130 + X2118 + X356), X356 >= 0 mark(z) -{ 2 }-> a__p(a__fact(mark(X355))) :|: z = 1 + (1 + X355), X355 >= 0 mark(z) -{ 2 }-> a__p(a__add(mark(X1132), mark(X2120))) :|: z = 1 + (1 + X1132 + X2120), X2120 >= 0, X1132 >= 0 mark(z) -{ 2 }-> a__p(2) :|: z = 1 + 2 mark(z) -{ 2 }-> a__p(1) :|: z = 1 + 1 mark(z) -{ 2 }-> a__p(0) :|: z = 1 + 0 mark(z) -{ 2 }-> a__p(1 + mark(X359)) :|: z = 1 + (1 + X359), X359 >= 0 mark(z) -{ 2 }-> a__if(a__zero(mark(X181)), X2, X3) :|: X181 >= 0, X3 >= 0, X2 >= 0, z = 1 + (1 + X181) + X2 + X3 mark(z) -{ 2 }-> a__if(a__prod(mark(X182), mark(X273)), X2, X3) :|: z = 1 + (1 + X182 + X273) + X2 + X3, X273 >= 0, X3 >= 0, X182 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__if(a__p(mark(X183)), X2, X3) :|: X183 >= 0, z = 1 + (1 + X183) + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__if(a__if(mark(X180), X272, X329), X2, X3) :|: z = 1 + (1 + X180 + X272 + X329) + X2 + X3, X272 >= 0, X329 >= 0, X3 >= 0, X2 >= 0, X180 >= 0 mark(z) -{ 2 }-> a__if(a__fact(mark(X179)), X2, X3) :|: z = 1 + (1 + X179) + X2 + X3, X3 >= 0, X2 >= 0, X179 >= 0 mark(z) -{ 2 }-> a__if(a__add(mark(X184), mark(X274)), X2, X3) :|: X184 >= 0, X274 >= 0, X3 >= 0, X2 >= 0, z = 1 + (1 + X184 + X274) + X2 + X3 mark(z) -{ 2 }-> a__if(2, X2, X3) :|: z = 1 + 2 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__if(1, X2, X3) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__if(0, X2, X3) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__if(1 + mark(X185), X2, X3) :|: X185 >= 0, X3 >= 0, z = 1 + (1 + X185) + X2 + X3, X2 >= 0 mark(z) -{ 2 }-> a__fact(a__zero(mark(X174))) :|: X174 >= 0, z = 1 + (1 + X174) mark(z) -{ 2 }-> a__fact(a__prod(mark(X175), mark(X270))) :|: z = 1 + (1 + X175 + X270), X175 >= 0, X270 >= 0 mark(z) -{ 2 }-> a__fact(a__p(mark(X176))) :|: X176 >= 0, z = 1 + (1 + X176) mark(z) -{ 2 }-> a__fact(a__if(mark(X173), X269, X328)) :|: X269 >= 0, X173 >= 0, X328 >= 0, z = 1 + (1 + X173 + X269 + X328) mark(z) -{ 2 }-> a__fact(a__fact(mark(X172))) :|: X172 >= 0, z = 1 + (1 + X172) mark(z) -{ 2 }-> a__fact(a__add(mark(X177), mark(X271))) :|: z = 1 + (1 + X177 + X271), X177 >= 0, X271 >= 0 mark(z) -{ 2 }-> a__fact(2) :|: z = 1 + 2 mark(z) -{ 2 }-> a__fact(1) :|: z = 1 + 1 mark(z) -{ 2 }-> a__fact(0) :|: z = 1 + 0 mark(z) -{ 2 }-> a__fact(1 + mark(X178)) :|: z = 1 + (1 + X178), X178 >= 0 mark(z) -{ 1 }-> a__add(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> 2 :|: z = 2 mark(z) -{ 1 }-> 1 :|: z = 1 mark(z) -{ 1 }-> 0 :|: z = 0 mark(z) -{ 1 }-> 1 + mark(X) :|: z = 1 + X, X >= 0 ---------------------------------------- (37) InliningProof (UPPER BOUND(ID)) Inlined the following terminating rules on right-hand sides where appropriate: a__zero(z) -{ 1 }-> 1 :|: z = 1 + X, X >= 0 a__zero(z) -{ 1 }-> 2 :|: z = 0 a__zero(z) -{ 1 }-> 1 + X :|: X >= 0, z = X ---------------------------------------- (38) Obligation: Complexity RNTS consisting of the following rules: a__add(z, z') -{ 1 }-> mark(X) :|: z' = X, X >= 0, z = 0 a__add(z, z') -{ 1 }-> 1 + a__add(mark(X), mark(Y)) :|: z = 1 + X, z' = Y, Y >= 0, X >= 0 a__add(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__fact(z) -{ 2 }-> a__if(a__zero(a__zero(mark(X''))), 1 + 0, 1 + (1 + X'') + (1 + (1 + (1 + X'')))) :|: z = 1 + X'', X'' >= 0 a__fact(z) -{ 2 }-> a__if(a__zero(a__prod(mark(X1''), mark(X2''))), 1 + 0, 1 + (1 + X1'' + X2'') + (1 + (1 + (1 + X1'' + X2'')))) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0 a__fact(z) -{ 2 }-> a__if(a__zero(a__p(mark(X4))), 1 + 0, 1 + (1 + X4) + (1 + (1 + (1 + X4)))) :|: z = 1 + X4, X4 >= 0 a__fact(z) -{ 2 }-> a__if(a__zero(a__if(mark(X1'), X2', X3')), 1 + 0, 1 + (1 + X1' + X2' + X3') + (1 + (1 + (1 + X1' + X2' + X3')))) :|: X3' >= 0, X2' >= 0, z = 1 + X1' + X2' + X3', X1' >= 0 a__fact(z) -{ 2 }-> a__if(a__zero(a__fact(mark(X'))), 1 + 0, 1 + (1 + X') + (1 + (1 + (1 + X')))) :|: X' >= 0, z = 1 + X' a__fact(z) -{ 2 }-> a__if(a__zero(a__add(mark(X11), mark(X21))), 1 + 0, 1 + (1 + X11 + X21) + (1 + (1 + (1 + X11 + X21)))) :|: X11 >= 0, X21 >= 0, z = 1 + X11 + X21 a__fact(z) -{ 2 }-> a__if(a__zero(1 + mark(X5)), 1 + 0, 1 + (1 + X5) + (1 + (1 + (1 + X5)))) :|: X5 >= 0, z = 1 + X5 a__fact(z) -{ 3 }-> a__if(2, 1 + 0, 1 + 0 + (1 + (1 + 0))) :|: z = 0, 0 = 0 a__fact(z) -{ 3 }-> a__if(1, 1 + 0, 1 + 2 + (1 + (1 + 2))) :|: z = 2, 2 = 1 + X, X >= 0 a__fact(z) -{ 3 }-> a__if(1, 1 + 0, 1 + 1 + (1 + (1 + 1))) :|: z = 1, 1 = 1 + X, X >= 0 a__fact(z) -{ 3 }-> a__if(1 + X, 1 + 0, 1 + 2 + (1 + (1 + 2))) :|: z = 2, X >= 0, 2 = X a__fact(z) -{ 3 }-> a__if(1 + X, 1 + 0, 1 + 1 + (1 + (1 + 1))) :|: z = 1, X >= 0, 1 = X a__fact(z) -{ 3 }-> a__if(1 + X, 1 + 0, 1 + 0 + (1 + (1 + 0))) :|: z = 0, X >= 0, 0 = X a__fact(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__if(z, z', z'') -{ 1 }-> mark(X) :|: z = 2, z' = X, Y >= 0, z'' = Y, X >= 0 a__if(z, z', z'') -{ 1 }-> mark(Y) :|: z' = X, Y >= 0, z = 1, z'' = Y, X >= 0 a__if(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__p(z) -{ 1 }-> mark(X) :|: z = 1 + X, X >= 0 a__p(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__prod(z, z') -{ 1 }-> a__add(mark(Y), a__prod(mark(X), mark(Y))) :|: z = 1 + X, z' = Y, Y >= 0, X >= 0 a__prod(z, z') -{ 1 }-> 0 :|: z' = X, X >= 0, z = 0 a__prod(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__zero(z) -{ 1 }-> 2 :|: z = 0 a__zero(z) -{ 1 }-> 1 :|: z = 1 + X, X >= 0 a__zero(z) -{ 1 }-> 1 + X :|: X >= 0, z = X mark(z) -{ 2 }-> a__zero(a__zero(mark(X188))) :|: X188 >= 0, z = 1 + (1 + X188) mark(z) -{ 2 }-> a__zero(a__prod(mark(X189), mark(X276))) :|: X276 >= 0, z = 1 + (1 + X189 + X276), X189 >= 0 mark(z) -{ 2 }-> a__zero(a__p(mark(X190))) :|: z = 1 + (1 + X190), X190 >= 0 mark(z) -{ 2 }-> a__zero(a__if(mark(X187), X275, X330)) :|: X187 >= 0, X275 >= 0, z = 1 + (1 + X187 + X275 + X330), X330 >= 0 mark(z) -{ 2 }-> a__zero(a__fact(mark(X186))) :|: z = 1 + (1 + X186), X186 >= 0 mark(z) -{ 2 }-> a__zero(a__add(mark(X191), mark(X277))) :|: z = 1 + (1 + X191 + X277), X191 >= 0, X277 >= 0 mark(z) -{ 2 }-> a__zero(1 + mark(X192)) :|: X192 >= 0, z = 1 + (1 + X192) mark(z) -{ 1 }-> a__prod(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 2 }-> a__p(a__zero(mark(X357))) :|: z = 1 + (1 + X357), X357 >= 0 mark(z) -{ 2 }-> a__p(a__prod(mark(X1131), mark(X2119))) :|: z = 1 + (1 + X1131 + X2119), X2119 >= 0, X1131 >= 0 mark(z) -{ 2 }-> a__p(a__p(mark(X358))) :|: X358 >= 0, z = 1 + (1 + X358) mark(z) -{ 2 }-> a__p(a__if(mark(X1130), X2118, X356)) :|: X2118 >= 0, X1130 >= 0, z = 1 + (1 + X1130 + X2118 + X356), X356 >= 0 mark(z) -{ 2 }-> a__p(a__fact(mark(X355))) :|: z = 1 + (1 + X355), X355 >= 0 mark(z) -{ 2 }-> a__p(a__add(mark(X1132), mark(X2120))) :|: z = 1 + (1 + X1132 + X2120), X2120 >= 0, X1132 >= 0 mark(z) -{ 2 }-> a__p(2) :|: z = 1 + 2 mark(z) -{ 2 }-> a__p(1) :|: z = 1 + 1 mark(z) -{ 2 }-> a__p(0) :|: z = 1 + 0 mark(z) -{ 2 }-> a__p(1 + mark(X359)) :|: z = 1 + (1 + X359), X359 >= 0 mark(z) -{ 2 }-> a__if(a__zero(mark(X181)), X2, X3) :|: X181 >= 0, X3 >= 0, X2 >= 0, z = 1 + (1 + X181) + X2 + X3 mark(z) -{ 2 }-> a__if(a__prod(mark(X182), mark(X273)), X2, X3) :|: z = 1 + (1 + X182 + X273) + X2 + X3, X273 >= 0, X3 >= 0, X182 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__if(a__p(mark(X183)), X2, X3) :|: X183 >= 0, z = 1 + (1 + X183) + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__if(a__if(mark(X180), X272, X329), X2, X3) :|: z = 1 + (1 + X180 + X272 + X329) + X2 + X3, X272 >= 0, X329 >= 0, X3 >= 0, X2 >= 0, X180 >= 0 mark(z) -{ 2 }-> a__if(a__fact(mark(X179)), X2, X3) :|: z = 1 + (1 + X179) + X2 + X3, X3 >= 0, X2 >= 0, X179 >= 0 mark(z) -{ 2 }-> a__if(a__add(mark(X184), mark(X274)), X2, X3) :|: X184 >= 0, X274 >= 0, X3 >= 0, X2 >= 0, z = 1 + (1 + X184 + X274) + X2 + X3 mark(z) -{ 2 }-> a__if(2, X2, X3) :|: z = 1 + 2 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__if(1, X2, X3) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__if(0, X2, X3) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__if(1 + mark(X185), X2, X3) :|: X185 >= 0, X3 >= 0, z = 1 + (1 + X185) + X2 + X3, X2 >= 0 mark(z) -{ 2 }-> a__fact(a__zero(mark(X174))) :|: X174 >= 0, z = 1 + (1 + X174) mark(z) -{ 2 }-> a__fact(a__prod(mark(X175), mark(X270))) :|: z = 1 + (1 + X175 + X270), X175 >= 0, X270 >= 0 mark(z) -{ 2 }-> a__fact(a__p(mark(X176))) :|: X176 >= 0, z = 1 + (1 + X176) mark(z) -{ 2 }-> a__fact(a__if(mark(X173), X269, X328)) :|: X269 >= 0, X173 >= 0, X328 >= 0, z = 1 + (1 + X173 + X269 + X328) mark(z) -{ 2 }-> a__fact(a__fact(mark(X172))) :|: X172 >= 0, z = 1 + (1 + X172) mark(z) -{ 2 }-> a__fact(a__add(mark(X177), mark(X271))) :|: z = 1 + (1 + X177 + X271), X177 >= 0, X271 >= 0 mark(z) -{ 2 }-> a__fact(2) :|: z = 1 + 2 mark(z) -{ 2 }-> a__fact(1) :|: z = 1 + 1 mark(z) -{ 2 }-> a__fact(0) :|: z = 1 + 0 mark(z) -{ 2 }-> a__fact(1 + mark(X178)) :|: z = 1 + (1 + X178), X178 >= 0 mark(z) -{ 1 }-> a__add(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> 2 :|: z = 2 mark(z) -{ 3 }-> 2 :|: z = 1 + 0, 0 = 0 mark(z) -{ 1 }-> 1 :|: z = 1 mark(z) -{ 3 }-> 1 :|: z = 1 + 2, 2 = 1 + X, X >= 0 mark(z) -{ 3 }-> 1 :|: z = 1 + 1, 1 = 1 + X, X >= 0 mark(z) -{ 1 }-> 0 :|: z = 0 mark(z) -{ 3 }-> 1 + X :|: z = 1 + 0, X >= 0, 0 = X mark(z) -{ 3 }-> 1 + X :|: z = 1 + 2, X >= 0, 2 = X mark(z) -{ 3 }-> 1 + X :|: z = 1 + 1, X >= 0, 1 = X mark(z) -{ 1 }-> 1 + mark(X) :|: z = 1 + X, X >= 0 ---------------------------------------- (39) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (40) Obligation: Complexity RNTS consisting of the following rules: a__add(z, z') -{ 1 }-> mark(z') :|: z' >= 0, z = 0 a__add(z, z') -{ 1 }-> 1 + a__add(mark(z - 1), mark(z')) :|: z' >= 0, z - 1 >= 0 a__add(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 a__fact(z) -{ 2 }-> a__if(a__zero(a__zero(mark(z - 1))), 1 + 0, 1 + (1 + (z - 1)) + (1 + (1 + (1 + (z - 1))))) :|: z - 1 >= 0 a__fact(z) -{ 2 }-> a__if(a__zero(a__prod(mark(X1''), mark(X2''))), 1 + 0, 1 + (1 + X1'' + X2'') + (1 + (1 + (1 + X1'' + X2'')))) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0 a__fact(z) -{ 2 }-> a__if(a__zero(a__p(mark(z - 1))), 1 + 0, 1 + (1 + (z - 1)) + (1 + (1 + (1 + (z - 1))))) :|: z - 1 >= 0 a__fact(z) -{ 2 }-> a__if(a__zero(a__if(mark(X1'), X2', X3')), 1 + 0, 1 + (1 + X1' + X2' + X3') + (1 + (1 + (1 + X1' + X2' + X3')))) :|: X3' >= 0, X2' >= 0, z = 1 + X1' + X2' + X3', X1' >= 0 a__fact(z) -{ 2 }-> a__if(a__zero(a__fact(mark(z - 1))), 1 + 0, 1 + (1 + (z - 1)) + (1 + (1 + (1 + (z - 1))))) :|: z - 1 >= 0 a__fact(z) -{ 2 }-> a__if(a__zero(a__add(mark(X11), mark(X21))), 1 + 0, 1 + (1 + X11 + X21) + (1 + (1 + (1 + X11 + X21)))) :|: X11 >= 0, X21 >= 0, z = 1 + X11 + X21 a__fact(z) -{ 2 }-> a__if(a__zero(1 + mark(z - 1)), 1 + 0, 1 + (1 + (z - 1)) + (1 + (1 + (1 + (z - 1))))) :|: z - 1 >= 0 a__fact(z) -{ 3 }-> a__if(2, 1 + 0, 1 + 0 + (1 + (1 + 0))) :|: z = 0, 0 = 0 a__fact(z) -{ 3 }-> a__if(1, 1 + 0, 1 + 2 + (1 + (1 + 2))) :|: z = 2, 2 = 1 + X, X >= 0 a__fact(z) -{ 3 }-> a__if(1, 1 + 0, 1 + 1 + (1 + (1 + 1))) :|: z = 1, 1 = 1 + X, X >= 0 a__fact(z) -{ 3 }-> a__if(1 + X, 1 + 0, 1 + 2 + (1 + (1 + 2))) :|: z = 2, X >= 0, 2 = X a__fact(z) -{ 3 }-> a__if(1 + X, 1 + 0, 1 + 1 + (1 + (1 + 1))) :|: z = 1, X >= 0, 1 = X a__fact(z) -{ 3 }-> a__if(1 + X, 1 + 0, 1 + 0 + (1 + (1 + 0))) :|: z = 0, X >= 0, 0 = X a__fact(z) -{ 1 }-> 1 + z :|: z >= 0 a__if(z, z', z'') -{ 1 }-> mark(z') :|: z = 2, z'' >= 0, z' >= 0 a__if(z, z', z'') -{ 1 }-> mark(z'') :|: z'' >= 0, z = 1, z' >= 0 a__if(z, z', z'') -{ 1 }-> 1 + z + z' + z'' :|: z >= 0, z'' >= 0, z' >= 0 a__p(z) -{ 1 }-> mark(z - 1) :|: z - 1 >= 0 a__p(z) -{ 1 }-> 1 + z :|: z >= 0 a__prod(z, z') -{ 1 }-> a__add(mark(z'), a__prod(mark(z - 1), mark(z'))) :|: z' >= 0, z - 1 >= 0 a__prod(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0 a__prod(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 a__zero(z) -{ 1 }-> 2 :|: z = 0 a__zero(z) -{ 1 }-> 1 :|: z - 1 >= 0 a__zero(z) -{ 1 }-> 1 + z :|: z >= 0 mark(z) -{ 2 }-> a__zero(a__zero(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__zero(a__prod(mark(X189), mark(X276))) :|: X276 >= 0, z = 1 + (1 + X189 + X276), X189 >= 0 mark(z) -{ 2 }-> a__zero(a__p(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__zero(a__if(mark(X187), X275, X330)) :|: X187 >= 0, X275 >= 0, z = 1 + (1 + X187 + X275 + X330), X330 >= 0 mark(z) -{ 2 }-> a__zero(a__fact(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__zero(a__add(mark(X191), mark(X277))) :|: z = 1 + (1 + X191 + X277), X191 >= 0, X277 >= 0 mark(z) -{ 2 }-> a__zero(1 + mark(z - 2)) :|: z - 2 >= 0 mark(z) -{ 1 }-> a__prod(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 2 }-> a__p(a__zero(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__p(a__prod(mark(X1131), mark(X2119))) :|: z = 1 + (1 + X1131 + X2119), X2119 >= 0, X1131 >= 0 mark(z) -{ 2 }-> a__p(a__p(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__p(a__if(mark(X1130), X2118, X356)) :|: X2118 >= 0, X1130 >= 0, z = 1 + (1 + X1130 + X2118 + X356), X356 >= 0 mark(z) -{ 2 }-> a__p(a__fact(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__p(a__add(mark(X1132), mark(X2120))) :|: z = 1 + (1 + X1132 + X2120), X2120 >= 0, X1132 >= 0 mark(z) -{ 2 }-> a__p(2) :|: z = 1 + 2 mark(z) -{ 2 }-> a__p(1) :|: z = 1 + 1 mark(z) -{ 2 }-> a__p(0) :|: z = 1 + 0 mark(z) -{ 2 }-> a__p(1 + mark(z - 2)) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__if(a__zero(mark(X181)), X2, X3) :|: X181 >= 0, X3 >= 0, X2 >= 0, z = 1 + (1 + X181) + X2 + X3 mark(z) -{ 2 }-> a__if(a__prod(mark(X182), mark(X273)), X2, X3) :|: z = 1 + (1 + X182 + X273) + X2 + X3, X273 >= 0, X3 >= 0, X182 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__if(a__p(mark(X183)), X2, X3) :|: X183 >= 0, z = 1 + (1 + X183) + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__if(a__if(mark(X180), X272, X329), X2, X3) :|: z = 1 + (1 + X180 + X272 + X329) + X2 + X3, X272 >= 0, X329 >= 0, X3 >= 0, X2 >= 0, X180 >= 0 mark(z) -{ 2 }-> a__if(a__fact(mark(X179)), X2, X3) :|: z = 1 + (1 + X179) + X2 + X3, X3 >= 0, X2 >= 0, X179 >= 0 mark(z) -{ 2 }-> a__if(a__add(mark(X184), mark(X274)), X2, X3) :|: X184 >= 0, X274 >= 0, X3 >= 0, X2 >= 0, z = 1 + (1 + X184 + X274) + X2 + X3 mark(z) -{ 2 }-> a__if(2, X2, X3) :|: z = 1 + 2 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__if(1, X2, X3) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__if(0, X2, X3) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__if(1 + mark(X185), X2, X3) :|: X185 >= 0, X3 >= 0, z = 1 + (1 + X185) + X2 + X3, X2 >= 0 mark(z) -{ 2 }-> a__fact(a__zero(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__fact(a__prod(mark(X175), mark(X270))) :|: z = 1 + (1 + X175 + X270), X175 >= 0, X270 >= 0 mark(z) -{ 2 }-> a__fact(a__p(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__fact(a__if(mark(X173), X269, X328)) :|: X269 >= 0, X173 >= 0, X328 >= 0, z = 1 + (1 + X173 + X269 + X328) mark(z) -{ 2 }-> a__fact(a__fact(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__fact(a__add(mark(X177), mark(X271))) :|: z = 1 + (1 + X177 + X271), X177 >= 0, X271 >= 0 mark(z) -{ 2 }-> a__fact(2) :|: z = 1 + 2 mark(z) -{ 2 }-> a__fact(1) :|: z = 1 + 1 mark(z) -{ 2 }-> a__fact(0) :|: z = 1 + 0 mark(z) -{ 2 }-> a__fact(1 + mark(z - 2)) :|: z - 2 >= 0 mark(z) -{ 1 }-> a__add(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> 2 :|: z = 2 mark(z) -{ 3 }-> 2 :|: z = 1 + 0, 0 = 0 mark(z) -{ 1 }-> 1 :|: z = 1 mark(z) -{ 3 }-> 1 :|: z = 1 + 2, 2 = 1 + X, X >= 0 mark(z) -{ 3 }-> 1 :|: z = 1 + 1, 1 = 1 + X, X >= 0 mark(z) -{ 1 }-> 0 :|: z = 0 mark(z) -{ 3 }-> 1 + X :|: z = 1 + 0, X >= 0, 0 = X mark(z) -{ 3 }-> 1 + X :|: z = 1 + 2, X >= 0, 2 = X mark(z) -{ 3 }-> 1 + X :|: z = 1 + 1, X >= 0, 1 = X mark(z) -{ 1 }-> 1 + mark(z - 1) :|: z - 1 >= 0 ---------------------------------------- (41) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT ---------------------------------------- (42) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), A__ZERO(mark(z0)), MARK(z0)) A__FACT(z0) -> c1 A__ADD(0, z0) -> c2(MARK(z0)) A__ADD(s(z0), z1) -> c3(A__ADD(mark(z0), mark(z1)), MARK(z0)) A__ADD(s(z0), z1) -> c4(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__ADD(z0, z1) -> c5 A__PROD(0, z0) -> c6 A__PROD(s(z0), z1) -> c7(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), MARK(z1)) A__PROD(s(z0), z1) -> c8(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z0)) A__PROD(s(z0), z1) -> c9(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z1)) A__PROD(z0, z1) -> c10 A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__IF(z0, z1, z2) -> c13 A__ZERO(0) -> c14 A__ZERO(s(z0)) -> c15 A__ZERO(z0) -> c16 A__P(s(z0)) -> c17(MARK(z0)) A__P(z0) -> c18 MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(if(z0, z1, z2)) -> c20(A__IF(mark(z0), z1, z2), MARK(z0)) MARK(zero(z0)) -> c21(A__ZERO(mark(z0)), MARK(z0)) MARK(prod(z0, z1)) -> c22(A__PROD(mark(z0), mark(z1)), MARK(z0)) MARK(prod(z0, z1)) -> c23(A__PROD(mark(z0), mark(z1)), MARK(z1)) MARK(p(z0)) -> c24(A__P(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) MARK(0) -> c28 MARK(true) -> c29 MARK(false) -> c30 S tuples: A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), A__ZERO(mark(z0)), MARK(z0)) A__FACT(z0) -> c1 A__ADD(0, z0) -> c2(MARK(z0)) A__ADD(s(z0), z1) -> c3(A__ADD(mark(z0), mark(z1)), MARK(z0)) A__ADD(s(z0), z1) -> c4(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__ADD(z0, z1) -> c5 A__PROD(0, z0) -> c6 A__PROD(s(z0), z1) -> c7(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), MARK(z1)) A__PROD(s(z0), z1) -> c8(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z0)) A__PROD(s(z0), z1) -> c9(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z1)) A__PROD(z0, z1) -> c10 A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__IF(z0, z1, z2) -> c13 A__ZERO(0) -> c14 A__ZERO(s(z0)) -> c15 A__ZERO(z0) -> c16 A__P(s(z0)) -> c17(MARK(z0)) A__P(z0) -> c18 MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(if(z0, z1, z2)) -> c20(A__IF(mark(z0), z1, z2), MARK(z0)) MARK(zero(z0)) -> c21(A__ZERO(mark(z0)), MARK(z0)) MARK(prod(z0, z1)) -> c22(A__PROD(mark(z0), mark(z1)), MARK(z0)) MARK(prod(z0, z1)) -> c23(A__PROD(mark(z0), mark(z1)), MARK(z1)) MARK(p(z0)) -> c24(A__P(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) MARK(0) -> c28 MARK(true) -> c29 MARK(false) -> c30 K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__FACT_1, A__ADD_2, A__PROD_2, A__IF_3, A__ZERO_1, A__P_1, MARK_1 Compound Symbols: c_3, c1, c2_1, c3_2, c4_2, c5, c6, c7_2, c8_3, c9_3, c10, c11_1, c12_1, c13, c14, c15, c16, c17_1, c18, c19_2, c20_2, c21_2, c22_2, c23_2, c24_2, c25_2, c26_2, c27_1, c28, c29, c30 ---------------------------------------- (43) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 12 trailing nodes: MARK(0) -> c28 A__PROD(z0, z1) -> c10 A__IF(z0, z1, z2) -> c13 MARK(true) -> c29 MARK(false) -> c30 A__ZERO(z0) -> c16 A__FACT(z0) -> c1 A__ZERO(s(z0)) -> c15 A__P(z0) -> c18 A__PROD(0, z0) -> c6 A__ZERO(0) -> c14 A__ADD(z0, z1) -> c5 ---------------------------------------- (44) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), A__ZERO(mark(z0)), MARK(z0)) A__ADD(0, z0) -> c2(MARK(z0)) A__ADD(s(z0), z1) -> c3(A__ADD(mark(z0), mark(z1)), MARK(z0)) A__ADD(s(z0), z1) -> c4(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__PROD(s(z0), z1) -> c7(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), MARK(z1)) A__PROD(s(z0), z1) -> c8(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z0)) A__PROD(s(z0), z1) -> c9(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z1)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(if(z0, z1, z2)) -> c20(A__IF(mark(z0), z1, z2), MARK(z0)) MARK(zero(z0)) -> c21(A__ZERO(mark(z0)), MARK(z0)) MARK(prod(z0, z1)) -> c22(A__PROD(mark(z0), mark(z1)), MARK(z0)) MARK(prod(z0, z1)) -> c23(A__PROD(mark(z0), mark(z1)), MARK(z1)) MARK(p(z0)) -> c24(A__P(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) S tuples: A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), A__ZERO(mark(z0)), MARK(z0)) A__ADD(0, z0) -> c2(MARK(z0)) A__ADD(s(z0), z1) -> c3(A__ADD(mark(z0), mark(z1)), MARK(z0)) A__ADD(s(z0), z1) -> c4(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__PROD(s(z0), z1) -> c7(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), MARK(z1)) A__PROD(s(z0), z1) -> c8(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z0)) A__PROD(s(z0), z1) -> c9(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z1)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(if(z0, z1, z2)) -> c20(A__IF(mark(z0), z1, z2), MARK(z0)) MARK(zero(z0)) -> c21(A__ZERO(mark(z0)), MARK(z0)) MARK(prod(z0, z1)) -> c22(A__PROD(mark(z0), mark(z1)), MARK(z0)) MARK(prod(z0, z1)) -> c23(A__PROD(mark(z0), mark(z1)), MARK(z1)) MARK(p(z0)) -> c24(A__P(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__FACT_1, A__ADD_2, A__PROD_2, A__IF_3, A__P_1, MARK_1 Compound Symbols: c_3, c2_1, c3_2, c4_2, c7_2, c8_3, c9_3, c11_1, c12_1, c17_1, c19_2, c20_2, c21_2, c22_2, c23_2, c24_2, c25_2, c26_2, c27_1 ---------------------------------------- (45) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (46) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__ADD(s(z0), z1) -> c3(A__ADD(mark(z0), mark(z1)), MARK(z0)) A__ADD(s(z0), z1) -> c4(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__PROD(s(z0), z1) -> c7(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), MARK(z1)) A__PROD(s(z0), z1) -> c8(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z0)) A__PROD(s(z0), z1) -> c9(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z1)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(if(z0, z1, z2)) -> c20(A__IF(mark(z0), z1, z2), MARK(z0)) MARK(prod(z0, z1)) -> c22(A__PROD(mark(z0), mark(z1)), MARK(z0)) MARK(prod(z0, z1)) -> c23(A__PROD(mark(z0), mark(z1)), MARK(z1)) MARK(p(z0)) -> c24(A__P(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__ADD(s(z0), z1) -> c3(A__ADD(mark(z0), mark(z1)), MARK(z0)) A__ADD(s(z0), z1) -> c4(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__PROD(s(z0), z1) -> c7(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), MARK(z1)) A__PROD(s(z0), z1) -> c8(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z0)) A__PROD(s(z0), z1) -> c9(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z1)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(if(z0, z1, z2)) -> c20(A__IF(mark(z0), z1, z2), MARK(z0)) MARK(prod(z0, z1)) -> c22(A__PROD(mark(z0), mark(z1)), MARK(z0)) MARK(prod(z0, z1)) -> c23(A__PROD(mark(z0), mark(z1)), MARK(z1)) MARK(p(z0)) -> c24(A__P(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__PROD_2, A__IF_3, A__P_1, MARK_1, A__FACT_1 Compound Symbols: c2_1, c3_2, c4_2, c7_2, c8_3, c9_3, c11_1, c12_1, c17_1, c19_2, c20_2, c22_2, c23_2, c24_2, c25_2, c26_2, c27_1, c_2, c21_1 ---------------------------------------- (47) CdtToCpxRelTrsProof (BOTH BOUNDS(ID, ID)) Converted S to standard rules, and D \ S as well as R to relative rules. ---------------------------------------- (48) 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__ADD(0, z0) -> c2(MARK(z0)) A__ADD(s(z0), z1) -> c3(A__ADD(mark(z0), mark(z1)), MARK(z0)) A__ADD(s(z0), z1) -> c4(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__PROD(s(z0), z1) -> c7(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), MARK(z1)) A__PROD(s(z0), z1) -> c8(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z0)) A__PROD(s(z0), z1) -> c9(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z1)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(if(z0, z1, z2)) -> c20(A__IF(mark(z0), z1, z2), MARK(z0)) MARK(prod(z0, z1)) -> c22(A__PROD(mark(z0), mark(z1)), MARK(z0)) MARK(prod(z0, z1)) -> c23(A__PROD(mark(z0), mark(z1)), MARK(z1)) MARK(p(z0)) -> c24(A__P(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) The (relative) TRS S consists of the following rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Rewrite Strategy: INNERMOST ---------------------------------------- (49) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (50) 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__ADD(0, z0) -> c2(MARK(z0)) A__ADD(s(z0), z1) -> c3(A__ADD(mark(z0), mark(z1)), MARK(z0)) A__ADD(s(z0), z1) -> c4(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__PROD(s(z0), z1) -> c7(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), MARK(z1)) A__PROD(s(z0), z1) -> c8(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z0)) A__PROD(s(z0), z1) -> c9(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z1)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(if(z0, z1, z2)) -> c20(A__IF(mark(z0), z1, z2), MARK(z0)) MARK(prod(z0, z1)) -> c22(A__PROD(mark(z0), mark(z1)), MARK(z0)) MARK(prod(z0, z1)) -> c23(A__PROD(mark(z0), mark(z1)), MARK(z1)) MARK(p(z0)) -> c24(A__P(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (51) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (52) 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__ADD(0, z0) -> c2(MARK(z0)) [1] A__ADD(s(z0), z1) -> c3(A__ADD(mark(z0), mark(z1)), MARK(z0)) [1] A__ADD(s(z0), z1) -> c4(A__ADD(mark(z0), mark(z1)), MARK(z1)) [1] A__PROD(s(z0), z1) -> c7(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), MARK(z1)) [1] A__PROD(s(z0), z1) -> c8(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z0)) [1] A__PROD(s(z0), z1) -> c9(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z1)) [1] A__IF(true, z0, z1) -> c11(MARK(z0)) [1] A__IF(false, z0, z1) -> c12(MARK(z1)) [1] A__P(s(z0)) -> c17(MARK(z0)) [1] MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) [1] MARK(if(z0, z1, z2)) -> c20(A__IF(mark(z0), z1, z2), MARK(z0)) [1] MARK(prod(z0, z1)) -> c22(A__PROD(mark(z0), mark(z1)), MARK(z0)) [1] MARK(prod(z0, z1)) -> c23(A__PROD(mark(z0), mark(z1)), MARK(z1)) [1] MARK(p(z0)) -> c24(A__P(mark(z0)), MARK(z0)) [1] MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) [1] MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) [1] MARK(s(z0)) -> c27(MARK(z0)) [1] A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), MARK(z0)) [1] MARK(zero(z0)) -> c21(MARK(z0)) [1] a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) [0] a__fact(z0) -> fact(z0) [0] a__add(0, z0) -> mark(z0) [0] a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) [0] a__add(z0, z1) -> add(z0, z1) [0] a__prod(0, z0) -> 0 [0] a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) [0] a__prod(z0, z1) -> prod(z0, z1) [0] a__if(true, z0, z1) -> mark(z0) [0] a__if(false, z0, z1) -> mark(z1) [0] a__if(z0, z1, z2) -> if(z0, z1, z2) [0] a__zero(0) -> true [0] a__zero(s(z0)) -> false [0] a__zero(z0) -> zero(z0) [0] a__p(s(z0)) -> mark(z0) [0] a__p(z0) -> p(z0) [0] mark(fact(z0)) -> a__fact(mark(z0)) [0] mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) [0] mark(zero(z0)) -> a__zero(mark(z0)) [0] mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) [0] mark(p(z0)) -> a__p(mark(z0)) [0] mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) [0] mark(s(z0)) -> s(mark(z0)) [0] mark(0) -> 0 [0] mark(true) -> true [0] mark(false) -> false [0] Rewrite Strategy: INNERMOST ---------------------------------------- (53) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (54) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: A__ADD(0, z0) -> c2(MARK(z0)) [1] A__ADD(s(z0), z1) -> c3(A__ADD(mark(z0), mark(z1)), MARK(z0)) [1] A__ADD(s(z0), z1) -> c4(A__ADD(mark(z0), mark(z1)), MARK(z1)) [1] A__PROD(s(z0), z1) -> c7(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), MARK(z1)) [1] A__PROD(s(z0), z1) -> c8(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z0)) [1] A__PROD(s(z0), z1) -> c9(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z1)) [1] A__IF(true, z0, z1) -> c11(MARK(z0)) [1] A__IF(false, z0, z1) -> c12(MARK(z1)) [1] A__P(s(z0)) -> c17(MARK(z0)) [1] MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) [1] MARK(if(z0, z1, z2)) -> c20(A__IF(mark(z0), z1, z2), MARK(z0)) [1] MARK(prod(z0, z1)) -> c22(A__PROD(mark(z0), mark(z1)), MARK(z0)) [1] MARK(prod(z0, z1)) -> c23(A__PROD(mark(z0), mark(z1)), MARK(z1)) [1] MARK(p(z0)) -> c24(A__P(mark(z0)), MARK(z0)) [1] MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) [1] MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) [1] MARK(s(z0)) -> c27(MARK(z0)) [1] A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), MARK(z0)) [1] MARK(zero(z0)) -> c21(MARK(z0)) [1] a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) [0] a__fact(z0) -> fact(z0) [0] a__add(0, z0) -> mark(z0) [0] a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) [0] a__add(z0, z1) -> add(z0, z1) [0] a__prod(0, z0) -> 0 [0] a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) [0] a__prod(z0, z1) -> prod(z0, z1) [0] a__if(true, z0, z1) -> mark(z0) [0] a__if(false, z0, z1) -> mark(z1) [0] a__if(z0, z1, z2) -> if(z0, z1, z2) [0] a__zero(0) -> true [0] a__zero(s(z0)) -> false [0] a__zero(z0) -> zero(z0) [0] a__p(s(z0)) -> mark(z0) [0] a__p(z0) -> p(z0) [0] mark(fact(z0)) -> a__fact(mark(z0)) [0] mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) [0] mark(zero(z0)) -> a__zero(mark(z0)) [0] mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) [0] mark(p(z0)) -> a__p(mark(z0)) [0] mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) [0] mark(s(z0)) -> s(mark(z0)) [0] mark(0) -> 0 [0] mark(true) -> true [0] mark(false) -> false [0] The TRS has the following type information: A__ADD :: 0:s:true:false:fact:if:prod:p:add:zero -> 0:s:true:false:fact:if:prod:p:add:zero -> c2:c3:c4 0 :: 0:s:true:false:fact:if:prod:p:add:zero c2 :: c19:c20:c22:c23:c24:c25:c26:c27:c21 -> c2:c3:c4 MARK :: 0:s:true:false:fact:if:prod:p:add:zero -> c19:c20:c22:c23:c24:c25:c26:c27:c21 s :: 0:s:true:false:fact:if:prod:p:add:zero -> 0:s:true:false:fact:if:prod:p:add:zero c3 :: c2:c3:c4 -> c19:c20:c22:c23:c24:c25:c26:c27:c21 -> c2:c3:c4 mark :: 0:s:true:false:fact:if:prod:p:add:zero -> 0:s:true:false:fact:if:prod:p:add:zero c4 :: c2:c3:c4 -> c19:c20:c22:c23:c24:c25:c26:c27:c21 -> c2:c3:c4 A__PROD :: 0:s:true:false:fact:if:prod:p:add:zero -> 0:s:true:false:fact:if:prod:p:add:zero -> c7:c8:c9 c7 :: c2:c3:c4 -> c19:c20:c22:c23:c24:c25:c26:c27:c21 -> c7:c8:c9 a__prod :: 0:s:true:false:fact:if:prod:p:add:zero -> 0:s:true:false:fact:if:prod:p:add:zero -> 0:s:true:false:fact:if:prod:p:add:zero c8 :: c2:c3:c4 -> c7:c8:c9 -> c19:c20:c22:c23:c24:c25:c26:c27:c21 -> c7:c8:c9 c9 :: c2:c3:c4 -> c7:c8:c9 -> c19:c20:c22:c23:c24:c25:c26:c27:c21 -> c7:c8:c9 A__IF :: 0:s:true:false:fact:if:prod:p:add:zero -> 0:s:true:false:fact:if:prod:p:add:zero -> 0:s:true:false:fact:if:prod:p:add:zero -> c11:c12 true :: 0:s:true:false:fact:if:prod:p:add:zero c11 :: c19:c20:c22:c23:c24:c25:c26:c27:c21 -> c11:c12 false :: 0:s:true:false:fact:if:prod:p:add:zero c12 :: c19:c20:c22:c23:c24:c25:c26:c27:c21 -> c11:c12 A__P :: 0:s:true:false:fact:if:prod:p:add:zero -> c17 c17 :: c19:c20:c22:c23:c24:c25:c26:c27:c21 -> c17 fact :: 0:s:true:false:fact:if:prod:p:add:zero -> 0:s:true:false:fact:if:prod:p:add:zero c19 :: c -> c19:c20:c22:c23:c24:c25:c26:c27:c21 -> c19:c20:c22:c23:c24:c25:c26:c27:c21 A__FACT :: 0:s:true:false:fact:if:prod:p:add:zero -> c if :: 0:s:true:false:fact:if:prod:p:add:zero -> 0:s:true:false:fact:if:prod:p:add:zero -> 0:s:true:false:fact:if:prod:p:add:zero -> 0:s:true:false:fact:if:prod:p:add:zero c20 :: c11:c12 -> c19:c20:c22:c23:c24:c25:c26:c27:c21 -> c19:c20:c22:c23:c24:c25:c26:c27:c21 prod :: 0:s:true:false:fact:if:prod:p:add:zero -> 0:s:true:false:fact:if:prod:p:add:zero -> 0:s:true:false:fact:if:prod:p:add:zero c22 :: c7:c8:c9 -> c19:c20:c22:c23:c24:c25:c26:c27:c21 -> c19:c20:c22:c23:c24:c25:c26:c27:c21 c23 :: c7:c8:c9 -> c19:c20:c22:c23:c24:c25:c26:c27:c21 -> c19:c20:c22:c23:c24:c25:c26:c27:c21 p :: 0:s:true:false:fact:if:prod:p:add:zero -> 0:s:true:false:fact:if:prod:p:add:zero c24 :: c17 -> c19:c20:c22:c23:c24:c25:c26:c27:c21 -> c19:c20:c22:c23:c24:c25:c26:c27:c21 add :: 0:s:true:false:fact:if:prod:p:add:zero -> 0:s:true:false:fact:if:prod:p:add:zero -> 0:s:true:false:fact:if:prod:p:add:zero c25 :: c2:c3:c4 -> c19:c20:c22:c23:c24:c25:c26:c27:c21 -> c19:c20:c22:c23:c24:c25:c26:c27:c21 c26 :: c2:c3:c4 -> c19:c20:c22:c23:c24:c25:c26:c27:c21 -> c19:c20:c22:c23:c24:c25:c26:c27:c21 c27 :: c19:c20:c22:c23:c24:c25:c26:c27:c21 -> c19:c20:c22:c23:c24:c25:c26:c27:c21 c :: c11:c12 -> c19:c20:c22:c23:c24:c25:c26:c27:c21 -> c a__zero :: 0:s:true:false:fact:if:prod:p:add:zero -> 0:s:true:false:fact:if:prod:p:add:zero zero :: 0:s:true:false:fact:if:prod:p:add:zero -> 0:s:true:false:fact:if:prod:p:add:zero c21 :: c19:c20:c22:c23:c24:c25:c26:c27:c21 -> c19:c20:c22:c23:c24:c25:c26:c27:c21 a__fact :: 0:s:true:false:fact:if:prod:p:add:zero -> 0:s:true:false:fact:if:prod:p:add:zero a__if :: 0:s:true:false:fact:if:prod:p:add:zero -> 0:s:true:false:fact:if:prod:p:add:zero -> 0:s:true:false:fact:if:prod:p:add:zero -> 0:s:true:false:fact:if:prod:p:add:zero a__add :: 0:s:true:false:fact:if:prod:p:add:zero -> 0:s:true:false:fact:if:prod:p:add:zero -> 0:s:true:false:fact:if:prod:p:add:zero a__p :: 0:s:true:false:fact:if:prod:p:add:zero -> 0:s:true:false:fact:if:prod:p:add:zero Rewrite Strategy: INNERMOST ---------------------------------------- (55) 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__ADD_2 A__PROD_2 A__IF_3 A__P_1 MARK_1 A__FACT_1 (c) The following functions are completely defined: a__fact_1 a__add_2 a__prod_2 a__if_3 a__zero_1 a__p_1 mark_1 Due to the following rules being added: a__fact(v0) -> null_a__fact [0] a__add(v0, v1) -> null_a__add [0] a__prod(v0, v1) -> null_a__prod [0] a__if(v0, v1, v2) -> null_a__if [0] a__zero(v0) -> null_a__zero [0] a__p(v0) -> null_a__p [0] mark(v0) -> null_mark [0] And the following fresh constants: null_a__fact, null_a__add, null_a__prod, null_a__if, null_a__zero, null_a__p, null_mark, const, const1, const2, const3, const4, const5 ---------------------------------------- (56) 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__ADD(0, z0) -> c2(MARK(z0)) [1] A__ADD(s(z0), z1) -> c3(A__ADD(mark(z0), mark(z1)), MARK(z0)) [1] A__ADD(s(z0), z1) -> c4(A__ADD(mark(z0), mark(z1)), MARK(z1)) [1] A__PROD(s(z0), z1) -> c7(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), MARK(z1)) [1] A__PROD(s(z0), z1) -> c8(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z0)) [1] A__PROD(s(z0), z1) -> c9(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z1)) [1] A__IF(true, z0, z1) -> c11(MARK(z0)) [1] A__IF(false, z0, z1) -> c12(MARK(z1)) [1] A__P(s(z0)) -> c17(MARK(z0)) [1] MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) [1] MARK(if(z0, z1, z2)) -> c20(A__IF(mark(z0), z1, z2), MARK(z0)) [1] MARK(prod(z0, z1)) -> c22(A__PROD(mark(z0), mark(z1)), MARK(z0)) [1] MARK(prod(z0, z1)) -> c23(A__PROD(mark(z0), mark(z1)), MARK(z1)) [1] MARK(p(z0)) -> c24(A__P(mark(z0)), MARK(z0)) [1] MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) [1] MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) [1] MARK(s(z0)) -> c27(MARK(z0)) [1] A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), MARK(z0)) [1] MARK(zero(z0)) -> c21(MARK(z0)) [1] a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) [0] a__fact(z0) -> fact(z0) [0] a__add(0, z0) -> mark(z0) [0] a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) [0] a__add(z0, z1) -> add(z0, z1) [0] a__prod(0, z0) -> 0 [0] a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) [0] a__prod(z0, z1) -> prod(z0, z1) [0] a__if(true, z0, z1) -> mark(z0) [0] a__if(false, z0, z1) -> mark(z1) [0] a__if(z0, z1, z2) -> if(z0, z1, z2) [0] a__zero(0) -> true [0] a__zero(s(z0)) -> false [0] a__zero(z0) -> zero(z0) [0] a__p(s(z0)) -> mark(z0) [0] a__p(z0) -> p(z0) [0] mark(fact(z0)) -> a__fact(mark(z0)) [0] mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) [0] mark(zero(z0)) -> a__zero(mark(z0)) [0] mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) [0] mark(p(z0)) -> a__p(mark(z0)) [0] mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) [0] mark(s(z0)) -> s(mark(z0)) [0] mark(0) -> 0 [0] mark(true) -> true [0] mark(false) -> false [0] a__fact(v0) -> null_a__fact [0] a__add(v0, v1) -> null_a__add [0] a__prod(v0, v1) -> null_a__prod [0] a__if(v0, v1, v2) -> null_a__if [0] a__zero(v0) -> null_a__zero [0] a__p(v0) -> null_a__p [0] mark(v0) -> null_mark [0] The TRS has the following type information: A__ADD :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> c2:c3:c4 0 :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark c2 :: c19:c20:c22:c23:c24:c25:c26:c27:c21 -> c2:c3:c4 MARK :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> c19:c20:c22:c23:c24:c25:c26:c27:c21 s :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark c3 :: c2:c3:c4 -> c19:c20:c22:c23:c24:c25:c26:c27:c21 -> c2:c3:c4 mark :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark c4 :: c2:c3:c4 -> c19:c20:c22:c23:c24:c25:c26:c27:c21 -> c2:c3:c4 A__PROD :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> c7:c8:c9 c7 :: c2:c3:c4 -> c19:c20:c22:c23:c24:c25:c26:c27:c21 -> c7:c8:c9 a__prod :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark c8 :: c2:c3:c4 -> c7:c8:c9 -> c19:c20:c22:c23:c24:c25:c26:c27:c21 -> c7:c8:c9 c9 :: c2:c3:c4 -> c7:c8:c9 -> c19:c20:c22:c23:c24:c25:c26:c27:c21 -> c7:c8:c9 A__IF :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> c11:c12 true :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark c11 :: c19:c20:c22:c23:c24:c25:c26:c27:c21 -> c11:c12 false :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark c12 :: c19:c20:c22:c23:c24:c25:c26:c27:c21 -> c11:c12 A__P :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> c17 c17 :: c19:c20:c22:c23:c24:c25:c26:c27:c21 -> c17 fact :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark c19 :: c -> c19:c20:c22:c23:c24:c25:c26:c27:c21 -> c19:c20:c22:c23:c24:c25:c26:c27:c21 A__FACT :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> c if :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark c20 :: c11:c12 -> c19:c20:c22:c23:c24:c25:c26:c27:c21 -> c19:c20:c22:c23:c24:c25:c26:c27:c21 prod :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark c22 :: c7:c8:c9 -> c19:c20:c22:c23:c24:c25:c26:c27:c21 -> c19:c20:c22:c23:c24:c25:c26:c27:c21 c23 :: c7:c8:c9 -> c19:c20:c22:c23:c24:c25:c26:c27:c21 -> c19:c20:c22:c23:c24:c25:c26:c27:c21 p :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark c24 :: c17 -> c19:c20:c22:c23:c24:c25:c26:c27:c21 -> c19:c20:c22:c23:c24:c25:c26:c27:c21 add :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark c25 :: c2:c3:c4 -> c19:c20:c22:c23:c24:c25:c26:c27:c21 -> c19:c20:c22:c23:c24:c25:c26:c27:c21 c26 :: c2:c3:c4 -> c19:c20:c22:c23:c24:c25:c26:c27:c21 -> c19:c20:c22:c23:c24:c25:c26:c27:c21 c27 :: c19:c20:c22:c23:c24:c25:c26:c27:c21 -> c19:c20:c22:c23:c24:c25:c26:c27:c21 c :: c11:c12 -> c19:c20:c22:c23:c24:c25:c26:c27:c21 -> c a__zero :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark zero :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark c21 :: c19:c20:c22:c23:c24:c25:c26:c27:c21 -> c19:c20:c22:c23:c24:c25:c26:c27:c21 a__fact :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark a__if :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark a__add :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark a__p :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark null_a__fact :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark null_a__add :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark null_a__prod :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark null_a__if :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark null_a__zero :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark null_a__p :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark null_mark :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark const :: c2:c3:c4 const1 :: c19:c20:c22:c23:c24:c25:c26:c27:c21 const2 :: c7:c8:c9 const3 :: c11:c12 const4 :: c17 const5 :: c Rewrite Strategy: INNERMOST ---------------------------------------- (57) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (58) 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__ADD(0, z0) -> c2(MARK(z0)) [1] A__ADD(s(z0), z1) -> c3(A__ADD(mark(z0), mark(z1)), MARK(z0)) [1] A__ADD(s(z0), z1) -> c4(A__ADD(mark(z0), mark(z1)), MARK(z1)) [1] A__PROD(s(z0), z1) -> c7(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), MARK(z1)) [1] A__PROD(s(z0), z1) -> c8(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z0)) [1] A__PROD(s(z0), z1) -> c9(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z1)) [1] A__IF(true, z0, z1) -> c11(MARK(z0)) [1] A__IF(false, z0, z1) -> c12(MARK(z1)) [1] A__P(s(z0)) -> c17(MARK(z0)) [1] MARK(fact(fact(z01518))) -> c19(A__FACT(a__fact(mark(z01518))), MARK(fact(z01518))) [1] MARK(fact(if(z01519, z1650, z2216))) -> c19(A__FACT(a__if(mark(z01519), z1650, z2216)), MARK(if(z01519, z1650, z2216))) [1] MARK(fact(zero(z01520))) -> c19(A__FACT(a__zero(mark(z01520))), MARK(zero(z01520))) [1] MARK(fact(prod(z01521, z1651))) -> c19(A__FACT(a__prod(mark(z01521), mark(z1651))), MARK(prod(z01521, z1651))) [1] MARK(fact(p(z01522))) -> c19(A__FACT(a__p(mark(z01522))), MARK(p(z01522))) [1] MARK(fact(add(z01523, z1652))) -> c19(A__FACT(a__add(mark(z01523), mark(z1652))), MARK(add(z01523, z1652))) [1] MARK(fact(s(z01524))) -> c19(A__FACT(s(mark(z01524))), MARK(s(z01524))) [1] MARK(fact(0)) -> c19(A__FACT(0), MARK(0)) [1] MARK(fact(true)) -> c19(A__FACT(true), MARK(true)) [1] MARK(fact(false)) -> c19(A__FACT(false), MARK(false)) [1] MARK(fact(z0)) -> c19(A__FACT(null_mark), MARK(z0)) [1] MARK(if(fact(z01525), z1, z2)) -> c20(A__IF(a__fact(mark(z01525)), z1, z2), MARK(fact(z01525))) [1] MARK(if(if(z01526, z1653, z2217), z1, z2)) -> c20(A__IF(a__if(mark(z01526), z1653, z2217), z1, z2), MARK(if(z01526, z1653, z2217))) [1] MARK(if(zero(z01527), z1, z2)) -> c20(A__IF(a__zero(mark(z01527)), z1, z2), MARK(zero(z01527))) [1] MARK(if(prod(z01528, z1654), z1, z2)) -> c20(A__IF(a__prod(mark(z01528), mark(z1654)), z1, z2), MARK(prod(z01528, z1654))) [1] MARK(if(p(z01529), z1, z2)) -> c20(A__IF(a__p(mark(z01529)), z1, z2), MARK(p(z01529))) [1] MARK(if(add(z01530, z1655), z1, z2)) -> c20(A__IF(a__add(mark(z01530), mark(z1655)), z1, z2), MARK(add(z01530, z1655))) [1] MARK(if(s(z01531), z1, z2)) -> c20(A__IF(s(mark(z01531)), z1, z2), MARK(s(z01531))) [1] MARK(if(0, z1, z2)) -> c20(A__IF(0, z1, z2), MARK(0)) [1] MARK(if(true, z1, z2)) -> c20(A__IF(true, z1, z2), MARK(true)) [1] MARK(if(false, z1, z2)) -> c20(A__IF(false, z1, z2), MARK(false)) [1] MARK(if(z0, z1, z2)) -> c20(A__IF(null_mark, z1, z2), MARK(z0)) [1] MARK(prod(z0, z1)) -> c22(A__PROD(mark(z0), mark(z1)), MARK(z0)) [1] MARK(prod(z0, z1)) -> c23(A__PROD(mark(z0), mark(z1)), MARK(z1)) [1] MARK(p(fact(z01700))) -> c24(A__P(a__fact(mark(z01700))), MARK(fact(z01700))) [1] MARK(p(if(z01701, z1728, z2242))) -> c24(A__P(a__if(mark(z01701), z1728, z2242)), MARK(if(z01701, z1728, z2242))) [1] MARK(p(zero(z01702))) -> c24(A__P(a__zero(mark(z01702))), MARK(zero(z01702))) [1] MARK(p(prod(z01703, z1729))) -> c24(A__P(a__prod(mark(z01703), mark(z1729))), MARK(prod(z01703, z1729))) [1] MARK(p(p(z01704))) -> c24(A__P(a__p(mark(z01704))), MARK(p(z01704))) [1] MARK(p(add(z01705, z1730))) -> c24(A__P(a__add(mark(z01705), mark(z1730))), MARK(add(z01705, z1730))) [1] MARK(p(s(z01706))) -> c24(A__P(s(mark(z01706))), MARK(s(z01706))) [1] MARK(p(0)) -> c24(A__P(0), MARK(0)) [1] MARK(p(true)) -> c24(A__P(true), MARK(true)) [1] MARK(p(false)) -> c24(A__P(false), MARK(false)) [1] MARK(p(z0)) -> c24(A__P(null_mark), MARK(z0)) [1] MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) [1] MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) [1] MARK(s(z0)) -> c27(MARK(z0)) [1] A__FACT(fact(z01875)) -> c(A__IF(a__zero(a__fact(mark(z01875))), s(0), prod(fact(z01875), fact(p(fact(z01875))))), MARK(fact(z01875))) [1] A__FACT(if(z01876, z1803, z2267)) -> c(A__IF(a__zero(a__if(mark(z01876), z1803, z2267)), s(0), prod(if(z01876, z1803, z2267), fact(p(if(z01876, z1803, z2267))))), MARK(if(z01876, z1803, z2267))) [1] A__FACT(zero(z01877)) -> c(A__IF(a__zero(a__zero(mark(z01877))), s(0), prod(zero(z01877), fact(p(zero(z01877))))), MARK(zero(z01877))) [1] A__FACT(prod(z01878, z1804)) -> c(A__IF(a__zero(a__prod(mark(z01878), mark(z1804))), s(0), prod(prod(z01878, z1804), fact(p(prod(z01878, z1804))))), MARK(prod(z01878, z1804))) [1] A__FACT(p(z01879)) -> c(A__IF(a__zero(a__p(mark(z01879))), s(0), prod(p(z01879), fact(p(p(z01879))))), MARK(p(z01879))) [1] A__FACT(add(z01880, z1805)) -> c(A__IF(a__zero(a__add(mark(z01880), mark(z1805))), s(0), prod(add(z01880, z1805), fact(p(add(z01880, z1805))))), MARK(add(z01880, z1805))) [1] A__FACT(s(z01881)) -> c(A__IF(a__zero(s(mark(z01881))), s(0), prod(s(z01881), fact(p(s(z01881))))), MARK(s(z01881))) [1] A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0)))), MARK(0)) [1] A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true)))), MARK(true)) [1] A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false)))), MARK(false)) [1] A__FACT(z0) -> c(A__IF(a__zero(null_mark), s(0), prod(z0, fact(p(z0)))), MARK(z0)) [1] MARK(zero(z0)) -> c21(MARK(z0)) [1] a__fact(fact(z01882)) -> a__if(a__zero(a__fact(mark(z01882))), s(0), prod(fact(z01882), fact(p(fact(z01882))))) [0] a__fact(if(z01883, z1806, z2268)) -> a__if(a__zero(a__if(mark(z01883), z1806, z2268)), s(0), prod(if(z01883, z1806, z2268), fact(p(if(z01883, z1806, z2268))))) [0] a__fact(zero(z01884)) -> a__if(a__zero(a__zero(mark(z01884))), s(0), prod(zero(z01884), fact(p(zero(z01884))))) [0] a__fact(prod(z01885, z1807)) -> a__if(a__zero(a__prod(mark(z01885), mark(z1807))), s(0), prod(prod(z01885, z1807), fact(p(prod(z01885, z1807))))) [0] a__fact(p(z01886)) -> a__if(a__zero(a__p(mark(z01886))), s(0), prod(p(z01886), fact(p(p(z01886))))) [0] a__fact(add(z01887, z1808)) -> a__if(a__zero(a__add(mark(z01887), mark(z1808))), s(0), prod(add(z01887, z1808), fact(p(add(z01887, z1808))))) [0] a__fact(s(z01888)) -> a__if(a__zero(s(mark(z01888))), s(0), prod(s(z01888), fact(p(s(z01888))))) [0] a__fact(0) -> a__if(a__zero(0), s(0), prod(0, fact(p(0)))) [0] a__fact(true) -> a__if(a__zero(true), s(0), prod(true, fact(p(true)))) [0] a__fact(false) -> a__if(a__zero(false), s(0), prod(false, fact(p(false)))) [0] a__fact(z0) -> a__if(a__zero(null_mark), s(0), prod(z0, fact(p(z0)))) [0] a__fact(z0) -> fact(z0) [0] a__add(0, z0) -> mark(z0) [0] a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) [0] a__add(z0, z1) -> add(z0, z1) [0] a__prod(0, z0) -> 0 [0] a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) [0] a__prod(z0, z1) -> prod(z0, z1) [0] a__if(true, z0, z1) -> mark(z0) [0] a__if(false, z0, z1) -> mark(z1) [0] a__if(z0, z1, z2) -> if(z0, z1, z2) [0] a__zero(0) -> true [0] a__zero(s(z0)) -> false [0] a__zero(z0) -> zero(z0) [0] a__p(s(z0)) -> mark(z0) [0] a__p(z0) -> p(z0) [0] mark(fact(fact(z02134))) -> a__fact(a__fact(mark(z02134))) [0] mark(fact(if(z02135, z1914, z2304))) -> a__fact(a__if(mark(z02135), z1914, z2304)) [0] mark(fact(zero(z02136))) -> a__fact(a__zero(mark(z02136))) [0] mark(fact(prod(z02137, z1915))) -> a__fact(a__prod(mark(z02137), mark(z1915))) [0] mark(fact(p(z02138))) -> a__fact(a__p(mark(z02138))) [0] mark(fact(add(z02139, z1916))) -> a__fact(a__add(mark(z02139), mark(z1916))) [0] mark(fact(s(z02140))) -> a__fact(s(mark(z02140))) [0] mark(fact(0)) -> a__fact(0) [0] mark(fact(true)) -> a__fact(true) [0] mark(fact(false)) -> a__fact(false) [0] mark(fact(z0)) -> a__fact(null_mark) [0] mark(if(fact(z02141), z1, z2)) -> a__if(a__fact(mark(z02141)), z1, z2) [0] mark(if(if(z02142, z1917, z2305), z1, z2)) -> a__if(a__if(mark(z02142), z1917, z2305), z1, z2) [0] mark(if(zero(z02143), z1, z2)) -> a__if(a__zero(mark(z02143)), z1, z2) [0] mark(if(prod(z02144, z1918), z1, z2)) -> a__if(a__prod(mark(z02144), mark(z1918)), z1, z2) [0] mark(if(p(z02145), z1, z2)) -> a__if(a__p(mark(z02145)), z1, z2) [0] mark(if(add(z02146, z1919), z1, z2)) -> a__if(a__add(mark(z02146), mark(z1919)), z1, z2) [0] mark(if(s(z02147), z1, z2)) -> a__if(s(mark(z02147)), z1, z2) [0] mark(if(0, z1, z2)) -> a__if(0, z1, z2) [0] mark(if(true, z1, z2)) -> a__if(true, z1, z2) [0] mark(if(false, z1, z2)) -> a__if(false, z1, z2) [0] mark(if(z0, z1, z2)) -> a__if(null_mark, z1, z2) [0] mark(zero(fact(z02148))) -> a__zero(a__fact(mark(z02148))) [0] mark(zero(if(z02149, z1920, z2306))) -> a__zero(a__if(mark(z02149), z1920, z2306)) [0] mark(zero(zero(z02150))) -> a__zero(a__zero(mark(z02150))) [0] mark(zero(prod(z02151, z1921))) -> a__zero(a__prod(mark(z02151), mark(z1921))) [0] mark(zero(p(z02152))) -> a__zero(a__p(mark(z02152))) [0] mark(zero(add(z02153, z1922))) -> a__zero(a__add(mark(z02153), mark(z1922))) [0] mark(zero(s(z02154))) -> a__zero(s(mark(z02154))) [0] mark(zero(0)) -> a__zero(0) [0] mark(zero(true)) -> a__zero(true) [0] mark(zero(false)) -> a__zero(false) [0] mark(zero(z0)) -> a__zero(null_mark) [0] mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) [0] mark(p(fact(z02239))) -> a__p(a__fact(mark(z02239))) [0] mark(p(if(z02240, z1959, z2319))) -> a__p(a__if(mark(z02240), z1959, z2319)) [0] mark(p(zero(z02241))) -> a__p(a__zero(mark(z02241))) [0] mark(p(prod(z02242, z1960))) -> a__p(a__prod(mark(z02242), mark(z1960))) [0] mark(p(p(z02243))) -> a__p(a__p(mark(z02243))) [0] mark(p(add(z02244, z1961))) -> a__p(a__add(mark(z02244), mark(z1961))) [0] mark(p(s(z02245))) -> a__p(s(mark(z02245))) [0] mark(p(0)) -> a__p(0) [0] mark(p(true)) -> a__p(true) [0] mark(p(false)) -> a__p(false) [0] mark(p(z0)) -> a__p(null_mark) [0] mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) [0] mark(s(z0)) -> s(mark(z0)) [0] mark(0) -> 0 [0] mark(true) -> true [0] mark(false) -> false [0] a__fact(v0) -> null_a__fact [0] a__add(v0, v1) -> null_a__add [0] a__prod(v0, v1) -> null_a__prod [0] a__if(v0, v1, v2) -> null_a__if [0] a__zero(v0) -> null_a__zero [0] a__p(v0) -> null_a__p [0] mark(v0) -> null_mark [0] The TRS has the following type information: A__ADD :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> c2:c3:c4 0 :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark c2 :: c19:c20:c22:c23:c24:c25:c26:c27:c21 -> c2:c3:c4 MARK :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> c19:c20:c22:c23:c24:c25:c26:c27:c21 s :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark c3 :: c2:c3:c4 -> c19:c20:c22:c23:c24:c25:c26:c27:c21 -> c2:c3:c4 mark :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark c4 :: c2:c3:c4 -> c19:c20:c22:c23:c24:c25:c26:c27:c21 -> c2:c3:c4 A__PROD :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> c7:c8:c9 c7 :: c2:c3:c4 -> c19:c20:c22:c23:c24:c25:c26:c27:c21 -> c7:c8:c9 a__prod :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark c8 :: c2:c3:c4 -> c7:c8:c9 -> c19:c20:c22:c23:c24:c25:c26:c27:c21 -> c7:c8:c9 c9 :: c2:c3:c4 -> c7:c8:c9 -> c19:c20:c22:c23:c24:c25:c26:c27:c21 -> c7:c8:c9 A__IF :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> c11:c12 true :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark c11 :: c19:c20:c22:c23:c24:c25:c26:c27:c21 -> c11:c12 false :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark c12 :: c19:c20:c22:c23:c24:c25:c26:c27:c21 -> c11:c12 A__P :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> c17 c17 :: c19:c20:c22:c23:c24:c25:c26:c27:c21 -> c17 fact :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark c19 :: c -> c19:c20:c22:c23:c24:c25:c26:c27:c21 -> c19:c20:c22:c23:c24:c25:c26:c27:c21 A__FACT :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> c if :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark c20 :: c11:c12 -> c19:c20:c22:c23:c24:c25:c26:c27:c21 -> c19:c20:c22:c23:c24:c25:c26:c27:c21 prod :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark c22 :: c7:c8:c9 -> c19:c20:c22:c23:c24:c25:c26:c27:c21 -> c19:c20:c22:c23:c24:c25:c26:c27:c21 c23 :: c7:c8:c9 -> c19:c20:c22:c23:c24:c25:c26:c27:c21 -> c19:c20:c22:c23:c24:c25:c26:c27:c21 p :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark c24 :: c17 -> c19:c20:c22:c23:c24:c25:c26:c27:c21 -> c19:c20:c22:c23:c24:c25:c26:c27:c21 add :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark c25 :: c2:c3:c4 -> c19:c20:c22:c23:c24:c25:c26:c27:c21 -> c19:c20:c22:c23:c24:c25:c26:c27:c21 c26 :: c2:c3:c4 -> c19:c20:c22:c23:c24:c25:c26:c27:c21 -> c19:c20:c22:c23:c24:c25:c26:c27:c21 c27 :: c19:c20:c22:c23:c24:c25:c26:c27:c21 -> c19:c20:c22:c23:c24:c25:c26:c27:c21 c :: c11:c12 -> c19:c20:c22:c23:c24:c25:c26:c27:c21 -> c a__zero :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark zero :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark c21 :: c19:c20:c22:c23:c24:c25:c26:c27:c21 -> c19:c20:c22:c23:c24:c25:c26:c27:c21 a__fact :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark a__if :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark a__add :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark a__p :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark null_a__fact :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark null_a__add :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark null_a__prod :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark null_a__if :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark null_a__zero :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark null_a__p :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark null_mark :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark const :: c2:c3:c4 const1 :: c19:c20:c22:c23:c24:c25:c26:c27:c21 const2 :: c7:c8:c9 const3 :: c11:c12 const4 :: c17 const5 :: c Rewrite Strategy: INNERMOST ---------------------------------------- (59) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: 0 => 0 true => 2 false => 1 null_a__fact => 0 null_a__add => 0 null_a__prod => 0 null_a__if => 0 null_a__zero => 0 null_a__p => 0 null_mark => 0 const => 0 const1 => 0 const2 => 0 const3 => 0 const4 => 0 const5 => 0 ---------------------------------------- (60) Obligation: Complexity RNTS consisting of the following rules: A__ADD(z, z') -{ 1 }-> 1 + MARK(z0) :|: z0 >= 0, z = 0, z' = z0 A__ADD(z, z') -{ 1 }-> 1 + A__ADD(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0 A__ADD(z, z') -{ 1 }-> 1 + A__ADD(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0 A__FACT(z) -{ 1 }-> 1 + A__IF(a__zero(a__zero(mark(z01877))), 1 + 0, 1 + (1 + z01877) + (1 + (1 + (1 + z01877)))) + MARK(1 + z01877) :|: z01877 >= 0, z = 1 + z01877 A__FACT(z) -{ 1 }-> 1 + A__IF(a__zero(a__prod(mark(z01878), mark(z1804))), 1 + 0, 1 + (1 + z01878 + z1804) + (1 + (1 + (1 + z01878 + z1804)))) + MARK(1 + z01878 + z1804) :|: z1804 >= 0, z01878 >= 0, z = 1 + z01878 + z1804 A__FACT(z) -{ 1 }-> 1 + A__IF(a__zero(a__p(mark(z01879))), 1 + 0, 1 + (1 + z01879) + (1 + (1 + (1 + z01879)))) + MARK(1 + z01879) :|: z01879 >= 0, z = 1 + z01879 A__FACT(z) -{ 1 }-> 1 + A__IF(a__zero(a__if(mark(z01876), z1803, z2267)), 1 + 0, 1 + (1 + z01876 + z1803 + z2267) + (1 + (1 + (1 + z01876 + z1803 + z2267)))) + MARK(1 + z01876 + z1803 + z2267) :|: z1803 >= 0, z = 1 + z01876 + z1803 + z2267, z2267 >= 0, z01876 >= 0 A__FACT(z) -{ 1 }-> 1 + A__IF(a__zero(a__fact(mark(z01875))), 1 + 0, 1 + (1 + z01875) + (1 + (1 + (1 + z01875)))) + MARK(1 + z01875) :|: z = 1 + z01875, z01875 >= 0 A__FACT(z) -{ 1 }-> 1 + A__IF(a__zero(a__add(mark(z01880), mark(z1805))), 1 + 0, 1 + (1 + z01880 + z1805) + (1 + (1 + (1 + z01880 + z1805)))) + MARK(1 + z01880 + z1805) :|: z01880 >= 0, z = 1 + z01880 + z1805, z1805 >= 0 A__FACT(z) -{ 1 }-> 1 + A__IF(a__zero(2), 1 + 0, 1 + 2 + (1 + (1 + 2))) + MARK(2) :|: z = 2 A__FACT(z) -{ 1 }-> 1 + A__IF(a__zero(1), 1 + 0, 1 + 1 + (1 + (1 + 1))) + MARK(1) :|: z = 1 A__FACT(z) -{ 1 }-> 1 + A__IF(a__zero(0), 1 + 0, 1 + z0 + (1 + (1 + z0))) + MARK(z0) :|: z = z0, z0 >= 0 A__FACT(z) -{ 1 }-> 1 + A__IF(a__zero(0), 1 + 0, 1 + 0 + (1 + (1 + 0))) + MARK(0) :|: z = 0 A__FACT(z) -{ 1 }-> 1 + A__IF(a__zero(1 + mark(z01881)), 1 + 0, 1 + (1 + z01881) + (1 + (1 + (1 + z01881)))) + MARK(1 + z01881) :|: z01881 >= 0, z = 1 + z01881 A__IF(z, z', z'') -{ 1 }-> 1 + MARK(z0) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1 A__IF(z, z', z'') -{ 1 }-> 1 + MARK(z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 A__P(z) -{ 1 }-> 1 + MARK(z0) :|: z = 1 + z0, z0 >= 0 A__PROD(z, z') -{ 1 }-> 1 + A__ADD(mark(z1), a__prod(mark(z0), mark(z1))) + MARK(z1) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0 A__PROD(z, z') -{ 1 }-> 1 + A__ADD(mark(z1), a__prod(mark(z0), mark(z1))) + A__PROD(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0 A__PROD(z, z') -{ 1 }-> 1 + A__ADD(mark(z1), a__prod(mark(z0), mark(z1))) + A__PROD(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0 MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__PROD(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__PROD(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__P(a__zero(mark(z01702))) + MARK(1 + z01702) :|: z = 1 + (1 + z01702), z01702 >= 0 MARK(z) -{ 1 }-> 1 + A__P(a__prod(mark(z01703), mark(z1729))) + MARK(1 + z01703 + z1729) :|: z1729 >= 0, z = 1 + (1 + z01703 + z1729), z01703 >= 0 MARK(z) -{ 1 }-> 1 + A__P(a__p(mark(z01704))) + MARK(1 + z01704) :|: z01704 >= 0, z = 1 + (1 + z01704) MARK(z) -{ 1 }-> 1 + A__P(a__if(mark(z01701), z1728, z2242)) + MARK(1 + z01701 + z1728 + z2242) :|: z = 1 + (1 + z01701 + z1728 + z2242), z01701 >= 0, z1728 >= 0, z2242 >= 0 MARK(z) -{ 1 }-> 1 + A__P(a__fact(mark(z01700))) + MARK(1 + z01700) :|: z = 1 + (1 + z01700), z01700 >= 0 MARK(z) -{ 1 }-> 1 + A__P(a__add(mark(z01705), mark(z1730))) + MARK(1 + z01705 + z1730) :|: z01705 >= 0, z = 1 + (1 + z01705 + z1730), z1730 >= 0 MARK(z) -{ 1 }-> 1 + A__P(2) + MARK(2) :|: z = 1 + 2 MARK(z) -{ 1 }-> 1 + A__P(1) + MARK(1) :|: z = 1 + 1 MARK(z) -{ 1 }-> 1 + A__P(0) + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__P(0) + MARK(0) :|: z = 1 + 0 MARK(z) -{ 1 }-> 1 + A__P(1 + mark(z01706)) + MARK(1 + z01706) :|: z = 1 + (1 + z01706), z01706 >= 0 MARK(z) -{ 1 }-> 1 + A__IF(a__zero(mark(z01527)), z1, z2) + MARK(1 + z01527) :|: z1 >= 0, z01527 >= 0, z = 1 + (1 + z01527) + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__IF(a__prod(mark(z01528), mark(z1654)), z1, z2) + MARK(1 + z01528 + z1654) :|: z01528 >= 0, z1654 >= 0, z1 >= 0, z = 1 + (1 + z01528 + z1654) + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__IF(a__p(mark(z01529)), z1, z2) + MARK(1 + z01529) :|: z1 >= 0, z = 1 + (1 + z01529) + z1 + z2, z2 >= 0, z01529 >= 0 MARK(z) -{ 1 }-> 1 + A__IF(a__if(mark(z01526), z1653, z2217), z1, z2) + MARK(1 + z01526 + z1653 + z2217) :|: z = 1 + (1 + z01526 + z1653 + z2217) + z1 + z2, z1 >= 0, z2217 >= 0, z01526 >= 0, z1653 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__IF(a__fact(mark(z01525)), z1, z2) + MARK(1 + z01525) :|: z = 1 + (1 + z01525) + z1 + z2, z1 >= 0, z01525 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__IF(a__add(mark(z01530), mark(z1655)), z1, z2) + MARK(1 + z01530 + z1655) :|: z01530 >= 0, z1 >= 0, z = 1 + (1 + z01530 + z1655) + z1 + z2, z1655 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__IF(2, z1, z2) + MARK(2) :|: z1 >= 0, z = 1 + 2 + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__IF(1, z1, z2) + MARK(1) :|: z1 >= 0, z = 1 + 1 + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__IF(0, z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__IF(0, z1, z2) + MARK(0) :|: z1 >= 0, z = 1 + 0 + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__IF(1 + mark(z01531), z1, z2) + MARK(1 + z01531) :|: z1 >= 0, z = 1 + (1 + z01531) + z1 + z2, z2 >= 0, z01531 >= 0 MARK(z) -{ 1 }-> 1 + A__FACT(a__zero(mark(z01520))) + MARK(1 + z01520) :|: z01520 >= 0, z = 1 + (1 + z01520) MARK(z) -{ 1 }-> 1 + A__FACT(a__prod(mark(z01521), mark(z1651))) + MARK(1 + z01521 + z1651) :|: z1651 >= 0, z = 1 + (1 + z01521 + z1651), z01521 >= 0 MARK(z) -{ 1 }-> 1 + A__FACT(a__p(mark(z01522))) + MARK(1 + z01522) :|: z = 1 + (1 + z01522), z01522 >= 0 MARK(z) -{ 1 }-> 1 + A__FACT(a__if(mark(z01519), z1650, z2216)) + MARK(1 + z01519 + z1650 + z2216) :|: z1650 >= 0, z2216 >= 0, z = 1 + (1 + z01519 + z1650 + z2216), z01519 >= 0 MARK(z) -{ 1 }-> 1 + A__FACT(a__fact(mark(z01518))) + MARK(1 + z01518) :|: z = 1 + (1 + z01518), z01518 >= 0 MARK(z) -{ 1 }-> 1 + A__FACT(a__add(mark(z01523), mark(z1652))) + MARK(1 + z01523 + z1652) :|: z = 1 + (1 + z01523 + z1652), z01523 >= 0, z1652 >= 0 MARK(z) -{ 1 }-> 1 + A__FACT(2) + MARK(2) :|: z = 1 + 2 MARK(z) -{ 1 }-> 1 + A__FACT(1) + MARK(1) :|: z = 1 + 1 MARK(z) -{ 1 }-> 1 + A__FACT(0) + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__FACT(0) + MARK(0) :|: z = 1 + 0 MARK(z) -{ 1 }-> 1 + A__FACT(1 + mark(z01524)) + MARK(1 + z01524) :|: z01524 >= 0, z = 1 + (1 + z01524) MARK(z) -{ 1 }-> 1 + A__ADD(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__ADD(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__add(z, z') -{ 0 }-> mark(z0) :|: z0 >= 0, z = 0, z' = z0 a__add(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__add(z, z') -{ 0 }-> 1 + a__add(mark(z0), mark(z1)) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0 a__add(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__fact(z) -{ 0 }-> a__if(a__zero(a__zero(mark(z01884))), 1 + 0, 1 + (1 + z01884) + (1 + (1 + (1 + z01884)))) :|: z01884 >= 0, z = 1 + z01884 a__fact(z) -{ 0 }-> a__if(a__zero(a__prod(mark(z01885), mark(z1807))), 1 + 0, 1 + (1 + z01885 + z1807) + (1 + (1 + (1 + z01885 + z1807)))) :|: z1807 >= 0, z = 1 + z01885 + z1807, z01885 >= 0 a__fact(z) -{ 0 }-> a__if(a__zero(a__p(mark(z01886))), 1 + 0, 1 + (1 + z01886) + (1 + (1 + (1 + z01886)))) :|: z = 1 + z01886, z01886 >= 0 a__fact(z) -{ 0 }-> a__if(a__zero(a__if(mark(z01883), z1806, z2268)), 1 + 0, 1 + (1 + z01883 + z1806 + z2268) + (1 + (1 + (1 + z01883 + z1806 + z2268)))) :|: z01883 >= 0, z1806 >= 0, z2268 >= 0, z = 1 + z01883 + z1806 + z2268 a__fact(z) -{ 0 }-> a__if(a__zero(a__fact(mark(z01882))), 1 + 0, 1 + (1 + z01882) + (1 + (1 + (1 + z01882)))) :|: z01882 >= 0, z = 1 + z01882 a__fact(z) -{ 0 }-> a__if(a__zero(a__add(mark(z01887), mark(z1808))), 1 + 0, 1 + (1 + z01887 + z1808) + (1 + (1 + (1 + z01887 + z1808)))) :|: z01887 >= 0, z = 1 + z01887 + z1808, z1808 >= 0 a__fact(z) -{ 0 }-> a__if(a__zero(2), 1 + 0, 1 + 2 + (1 + (1 + 2))) :|: z = 2 a__fact(z) -{ 0 }-> a__if(a__zero(1), 1 + 0, 1 + 1 + (1 + (1 + 1))) :|: z = 1 a__fact(z) -{ 0 }-> a__if(a__zero(0), 1 + 0, 1 + z0 + (1 + (1 + z0))) :|: z = z0, z0 >= 0 a__fact(z) -{ 0 }-> a__if(a__zero(0), 1 + 0, 1 + 0 + (1 + (1 + 0))) :|: z = 0 a__fact(z) -{ 0 }-> a__if(a__zero(1 + mark(z01888)), 1 + 0, 1 + (1 + z01888) + (1 + (1 + (1 + z01888)))) :|: z = 1 + z01888, z01888 >= 0 a__fact(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__fact(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__if(z, z', z'') -{ 0 }-> mark(z0) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1 a__if(z, z', z'') -{ 0 }-> mark(z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 a__if(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 a__if(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 a__p(z) -{ 0 }-> mark(z0) :|: z = 1 + z0, z0 >= 0 a__p(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__p(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__prod(z, z') -{ 0 }-> a__add(mark(z1), a__prod(mark(z0), mark(z1))) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0 a__prod(z, z') -{ 0 }-> 0 :|: z0 >= 0, z = 0, z' = z0 a__prod(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__prod(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__zero(z) -{ 0 }-> 2 :|: z = 0 a__zero(z) -{ 0 }-> 1 :|: z = 1 + z0, z0 >= 0 a__zero(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__zero(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 mark(z) -{ 0 }-> a__zero(a__zero(mark(z02150))) :|: z02150 >= 0, z = 1 + (1 + z02150) mark(z) -{ 0 }-> a__zero(a__prod(mark(z02151), mark(z1921))) :|: z1921 >= 0, z = 1 + (1 + z02151 + z1921), z02151 >= 0 mark(z) -{ 0 }-> a__zero(a__p(mark(z02152))) :|: z = 1 + (1 + z02152), z02152 >= 0 mark(z) -{ 0 }-> a__zero(a__if(mark(z02149), z1920, z2306)) :|: z2306 >= 0, z = 1 + (1 + z02149 + z1920 + z2306), z02149 >= 0, z1920 >= 0 mark(z) -{ 0 }-> a__zero(a__fact(mark(z02148))) :|: z = 1 + (1 + z02148), z02148 >= 0 mark(z) -{ 0 }-> a__zero(a__add(mark(z02153), mark(z1922))) :|: z02153 >= 0, z1922 >= 0, z = 1 + (1 + z02153 + z1922) mark(z) -{ 0 }-> a__zero(2) :|: z = 1 + 2 mark(z) -{ 0 }-> a__zero(1) :|: z = 1 + 1 mark(z) -{ 0 }-> a__zero(0) :|: z = 1 + 0 mark(z) -{ 0 }-> a__zero(0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__zero(1 + mark(z02154)) :|: z02154 >= 0, z = 1 + (1 + z02154) mark(z) -{ 0 }-> a__prod(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__p(a__zero(mark(z02241))) :|: z02241 >= 0, z = 1 + (1 + z02241) mark(z) -{ 0 }-> a__p(a__prod(mark(z02242), mark(z1960))) :|: z02242 >= 0, z = 1 + (1 + z02242 + z1960), z1960 >= 0 mark(z) -{ 0 }-> a__p(a__p(mark(z02243))) :|: z02243 >= 0, z = 1 + (1 + z02243) mark(z) -{ 0 }-> a__p(a__if(mark(z02240), z1959, z2319)) :|: z = 1 + (1 + z02240 + z1959 + z2319), z1959 >= 0, z02240 >= 0, z2319 >= 0 mark(z) -{ 0 }-> a__p(a__fact(mark(z02239))) :|: z02239 >= 0, z = 1 + (1 + z02239) mark(z) -{ 0 }-> a__p(a__add(mark(z02244), mark(z1961))) :|: z1961 >= 0, z02244 >= 0, z = 1 + (1 + z02244 + z1961) mark(z) -{ 0 }-> a__p(2) :|: z = 1 + 2 mark(z) -{ 0 }-> a__p(1) :|: z = 1 + 1 mark(z) -{ 0 }-> a__p(0) :|: z = 1 + 0 mark(z) -{ 0 }-> a__p(0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__p(1 + mark(z02245)) :|: z = 1 + (1 + z02245), z02245 >= 0 mark(z) -{ 0 }-> a__if(a__zero(mark(z02143)), z1, z2) :|: z = 1 + (1 + z02143) + z1 + z2, z1 >= 0, z02143 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__if(a__prod(mark(z02144), mark(z1918)), z1, z2) :|: z = 1 + (1 + z02144 + z1918) + z1 + z2, z1 >= 0, z02144 >= 0, z1918 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__if(a__p(mark(z02145)), z1, z2) :|: z1 >= 0, z02145 >= 0, z = 1 + (1 + z02145) + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__if(a__if(mark(z02142), z1917, z2305), z1, z2) :|: z1 >= 0, z2305 >= 0, z = 1 + (1 + z02142 + z1917 + z2305) + z1 + z2, z02142 >= 0, z2 >= 0, z1917 >= 0 mark(z) -{ 0 }-> a__if(a__fact(mark(z02141)), z1, z2) :|: z1 >= 0, z = 1 + (1 + z02141) + z1 + z2, z2 >= 0, z02141 >= 0 mark(z) -{ 0 }-> a__if(a__add(mark(z02146), mark(z1919)), z1, z2) :|: z = 1 + (1 + z02146 + z1919) + z1 + z2, z1 >= 0, z02146 >= 0, z1919 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__if(2, z1, z2) :|: z1 >= 0, z = 1 + 2 + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__if(1, z1, z2) :|: z1 >= 0, z = 1 + 1 + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__if(0, z1, z2) :|: z1 >= 0, z = 1 + 0 + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__if(0, z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__if(1 + mark(z02147), z1, z2) :|: z02147 >= 0, z1 >= 0, z = 1 + (1 + z02147) + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__fact(a__zero(mark(z02136))) :|: z = 1 + (1 + z02136), z02136 >= 0 mark(z) -{ 0 }-> a__fact(a__prod(mark(z02137), mark(z1915))) :|: z02137 >= 0, z = 1 + (1 + z02137 + z1915), z1915 >= 0 mark(z) -{ 0 }-> a__fact(a__p(mark(z02138))) :|: z = 1 + (1 + z02138), z02138 >= 0 mark(z) -{ 0 }-> a__fact(a__if(mark(z02135), z1914, z2304)) :|: z02135 >= 0, z1914 >= 0, z2304 >= 0, z = 1 + (1 + z02135 + z1914 + z2304) mark(z) -{ 0 }-> a__fact(a__fact(mark(z02134))) :|: z02134 >= 0, z = 1 + (1 + z02134) mark(z) -{ 0 }-> a__fact(a__add(mark(z02139), mark(z1916))) :|: z1916 >= 0, z = 1 + (1 + z02139 + z1916), z02139 >= 0 mark(z) -{ 0 }-> a__fact(2) :|: z = 1 + 2 mark(z) -{ 0 }-> a__fact(1) :|: z = 1 + 1 mark(z) -{ 0 }-> a__fact(0) :|: z = 1 + 0 mark(z) -{ 0 }-> a__fact(0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__fact(1 + mark(z02140)) :|: z = 1 + (1 + z02140), z02140 >= 0 mark(z) -{ 0 }-> a__add(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> 2 :|: z = 2 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 ---------------------------------------- (61) InliningProof (UPPER BOUND(ID)) Inlined the following terminating rules on right-hand sides where appropriate: a__zero(z) -{ 0 }-> 1 :|: z = 1 + z0, z0 >= 0 a__zero(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__zero(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__zero(z) -{ 0 }-> 2 :|: z = 0 ---------------------------------------- (62) Obligation: Complexity RNTS consisting of the following rules: A__ADD(z, z') -{ 1 }-> 1 + MARK(z0) :|: z0 >= 0, z = 0, z' = z0 A__ADD(z, z') -{ 1 }-> 1 + A__ADD(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0 A__ADD(z, z') -{ 1 }-> 1 + A__ADD(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0 A__FACT(z) -{ 1 }-> 1 + A__IF(a__zero(a__zero(mark(z01877))), 1 + 0, 1 + (1 + z01877) + (1 + (1 + (1 + z01877)))) + MARK(1 + z01877) :|: z01877 >= 0, z = 1 + z01877 A__FACT(z) -{ 1 }-> 1 + A__IF(a__zero(a__prod(mark(z01878), mark(z1804))), 1 + 0, 1 + (1 + z01878 + z1804) + (1 + (1 + (1 + z01878 + z1804)))) + MARK(1 + z01878 + z1804) :|: z1804 >= 0, z01878 >= 0, z = 1 + z01878 + z1804 A__FACT(z) -{ 1 }-> 1 + A__IF(a__zero(a__p(mark(z01879))), 1 + 0, 1 + (1 + z01879) + (1 + (1 + (1 + z01879)))) + MARK(1 + z01879) :|: z01879 >= 0, z = 1 + z01879 A__FACT(z) -{ 1 }-> 1 + A__IF(a__zero(a__if(mark(z01876), z1803, z2267)), 1 + 0, 1 + (1 + z01876 + z1803 + z2267) + (1 + (1 + (1 + z01876 + z1803 + z2267)))) + MARK(1 + z01876 + z1803 + z2267) :|: z1803 >= 0, z = 1 + z01876 + z1803 + z2267, z2267 >= 0, z01876 >= 0 A__FACT(z) -{ 1 }-> 1 + A__IF(a__zero(a__fact(mark(z01875))), 1 + 0, 1 + (1 + z01875) + (1 + (1 + (1 + z01875)))) + MARK(1 + z01875) :|: z = 1 + z01875, z01875 >= 0 A__FACT(z) -{ 1 }-> 1 + A__IF(a__zero(a__add(mark(z01880), mark(z1805))), 1 + 0, 1 + (1 + z01880 + z1805) + (1 + (1 + (1 + z01880 + z1805)))) + MARK(1 + z01880 + z1805) :|: z01880 >= 0, z = 1 + z01880 + z1805, z1805 >= 0 A__FACT(z) -{ 1 }-> 1 + A__IF(a__zero(1 + mark(z01881)), 1 + 0, 1 + (1 + z01881) + (1 + (1 + (1 + z01881)))) + MARK(1 + z01881) :|: z01881 >= 0, z = 1 + z01881 A__FACT(z) -{ 1 }-> 1 + A__IF(2, 1 + 0, 1 + z0 + (1 + (1 + z0))) + MARK(z0) :|: z = z0, z0 >= 0, 0 = 0 A__FACT(z) -{ 1 }-> 1 + A__IF(2, 1 + 0, 1 + 0 + (1 + (1 + 0))) + MARK(0) :|: z = 0, 0 = 0 A__FACT(z) -{ 1 }-> 1 + A__IF(1, 1 + 0, 1 + 2 + (1 + (1 + 2))) + MARK(2) :|: z = 2, 2 = 1 + z0, z0 >= 0 A__FACT(z) -{ 1 }-> 1 + A__IF(1, 1 + 0, 1 + 1 + (1 + (1 + 1))) + MARK(1) :|: z = 1, 1 = 1 + z0, z0 >= 0 A__FACT(z) -{ 1 }-> 1 + A__IF(0, 1 + 0, 1 + z0 + (1 + (1 + z0))) + MARK(z0) :|: z = z0, z0 >= 0, v0 >= 0, 0 = v0 A__FACT(z) -{ 1 }-> 1 + A__IF(0, 1 + 0, 1 + 2 + (1 + (1 + 2))) + MARK(2) :|: z = 2, v0 >= 0, 2 = v0 A__FACT(z) -{ 1 }-> 1 + A__IF(0, 1 + 0, 1 + 1 + (1 + (1 + 1))) + MARK(1) :|: z = 1, v0 >= 0, 1 = v0 A__FACT(z) -{ 1 }-> 1 + A__IF(0, 1 + 0, 1 + 0 + (1 + (1 + 0))) + MARK(0) :|: z = 0, v0 >= 0, 0 = v0 A__FACT(z) -{ 1 }-> 1 + A__IF(1 + z0, 1 + 0, 1 + 2 + (1 + (1 + 2))) + MARK(2) :|: z = 2, 2 = z0, z0 >= 0 A__FACT(z) -{ 1 }-> 1 + A__IF(1 + z0, 1 + 0, 1 + 1 + (1 + (1 + 1))) + MARK(1) :|: z = 1, 1 = z0, z0 >= 0 A__FACT(z) -{ 1 }-> 1 + A__IF(1 + z0, 1 + 0, 1 + 0 + (1 + (1 + 0))) + MARK(0) :|: z = 0, 0 = z0, z0 >= 0 A__FACT(z) -{ 1 }-> 1 + A__IF(1 + z0', 1 + 0, 1 + z0 + (1 + (1 + z0))) + MARK(z0) :|: z = z0, z0 >= 0, 0 = z0', z0' >= 0 A__IF(z, z', z'') -{ 1 }-> 1 + MARK(z0) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1 A__IF(z, z', z'') -{ 1 }-> 1 + MARK(z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 A__P(z) -{ 1 }-> 1 + MARK(z0) :|: z = 1 + z0, z0 >= 0 A__PROD(z, z') -{ 1 }-> 1 + A__ADD(mark(z1), a__prod(mark(z0), mark(z1))) + MARK(z1) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0 A__PROD(z, z') -{ 1 }-> 1 + A__ADD(mark(z1), a__prod(mark(z0), mark(z1))) + A__PROD(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0 A__PROD(z, z') -{ 1 }-> 1 + A__ADD(mark(z1), a__prod(mark(z0), mark(z1))) + A__PROD(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0 MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__PROD(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__PROD(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__P(a__zero(mark(z01702))) + MARK(1 + z01702) :|: z = 1 + (1 + z01702), z01702 >= 0 MARK(z) -{ 1 }-> 1 + A__P(a__prod(mark(z01703), mark(z1729))) + MARK(1 + z01703 + z1729) :|: z1729 >= 0, z = 1 + (1 + z01703 + z1729), z01703 >= 0 MARK(z) -{ 1 }-> 1 + A__P(a__p(mark(z01704))) + MARK(1 + z01704) :|: z01704 >= 0, z = 1 + (1 + z01704) MARK(z) -{ 1 }-> 1 + A__P(a__if(mark(z01701), z1728, z2242)) + MARK(1 + z01701 + z1728 + z2242) :|: z = 1 + (1 + z01701 + z1728 + z2242), z01701 >= 0, z1728 >= 0, z2242 >= 0 MARK(z) -{ 1 }-> 1 + A__P(a__fact(mark(z01700))) + MARK(1 + z01700) :|: z = 1 + (1 + z01700), z01700 >= 0 MARK(z) -{ 1 }-> 1 + A__P(a__add(mark(z01705), mark(z1730))) + MARK(1 + z01705 + z1730) :|: z01705 >= 0, z = 1 + (1 + z01705 + z1730), z1730 >= 0 MARK(z) -{ 1 }-> 1 + A__P(2) + MARK(2) :|: z = 1 + 2 MARK(z) -{ 1 }-> 1 + A__P(1) + MARK(1) :|: z = 1 + 1 MARK(z) -{ 1 }-> 1 + A__P(0) + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__P(0) + MARK(0) :|: z = 1 + 0 MARK(z) -{ 1 }-> 1 + A__P(1 + mark(z01706)) + MARK(1 + z01706) :|: z = 1 + (1 + z01706), z01706 >= 0 MARK(z) -{ 1 }-> 1 + A__IF(a__zero(mark(z01527)), z1, z2) + MARK(1 + z01527) :|: z1 >= 0, z01527 >= 0, z = 1 + (1 + z01527) + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__IF(a__prod(mark(z01528), mark(z1654)), z1, z2) + MARK(1 + z01528 + z1654) :|: z01528 >= 0, z1654 >= 0, z1 >= 0, z = 1 + (1 + z01528 + z1654) + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__IF(a__p(mark(z01529)), z1, z2) + MARK(1 + z01529) :|: z1 >= 0, z = 1 + (1 + z01529) + z1 + z2, z2 >= 0, z01529 >= 0 MARK(z) -{ 1 }-> 1 + A__IF(a__if(mark(z01526), z1653, z2217), z1, z2) + MARK(1 + z01526 + z1653 + z2217) :|: z = 1 + (1 + z01526 + z1653 + z2217) + z1 + z2, z1 >= 0, z2217 >= 0, z01526 >= 0, z1653 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__IF(a__fact(mark(z01525)), z1, z2) + MARK(1 + z01525) :|: z = 1 + (1 + z01525) + z1 + z2, z1 >= 0, z01525 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__IF(a__add(mark(z01530), mark(z1655)), z1, z2) + MARK(1 + z01530 + z1655) :|: z01530 >= 0, z1 >= 0, z = 1 + (1 + z01530 + z1655) + z1 + z2, z1655 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__IF(2, z1, z2) + MARK(2) :|: z1 >= 0, z = 1 + 2 + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__IF(1, z1, z2) + MARK(1) :|: z1 >= 0, z = 1 + 1 + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__IF(0, z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__IF(0, z1, z2) + MARK(0) :|: z1 >= 0, z = 1 + 0 + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__IF(1 + mark(z01531), z1, z2) + MARK(1 + z01531) :|: z1 >= 0, z = 1 + (1 + z01531) + z1 + z2, z2 >= 0, z01531 >= 0 MARK(z) -{ 1 }-> 1 + A__FACT(a__zero(mark(z01520))) + MARK(1 + z01520) :|: z01520 >= 0, z = 1 + (1 + z01520) MARK(z) -{ 1 }-> 1 + A__FACT(a__prod(mark(z01521), mark(z1651))) + MARK(1 + z01521 + z1651) :|: z1651 >= 0, z = 1 + (1 + z01521 + z1651), z01521 >= 0 MARK(z) -{ 1 }-> 1 + A__FACT(a__p(mark(z01522))) + MARK(1 + z01522) :|: z = 1 + (1 + z01522), z01522 >= 0 MARK(z) -{ 1 }-> 1 + A__FACT(a__if(mark(z01519), z1650, z2216)) + MARK(1 + z01519 + z1650 + z2216) :|: z1650 >= 0, z2216 >= 0, z = 1 + (1 + z01519 + z1650 + z2216), z01519 >= 0 MARK(z) -{ 1 }-> 1 + A__FACT(a__fact(mark(z01518))) + MARK(1 + z01518) :|: z = 1 + (1 + z01518), z01518 >= 0 MARK(z) -{ 1 }-> 1 + A__FACT(a__add(mark(z01523), mark(z1652))) + MARK(1 + z01523 + z1652) :|: z = 1 + (1 + z01523 + z1652), z01523 >= 0, z1652 >= 0 MARK(z) -{ 1 }-> 1 + A__FACT(2) + MARK(2) :|: z = 1 + 2 MARK(z) -{ 1 }-> 1 + A__FACT(1) + MARK(1) :|: z = 1 + 1 MARK(z) -{ 1 }-> 1 + A__FACT(0) + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__FACT(0) + MARK(0) :|: z = 1 + 0 MARK(z) -{ 1 }-> 1 + A__FACT(1 + mark(z01524)) + MARK(1 + z01524) :|: z01524 >= 0, z = 1 + (1 + z01524) MARK(z) -{ 1 }-> 1 + A__ADD(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__ADD(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__add(z, z') -{ 0 }-> mark(z0) :|: z0 >= 0, z = 0, z' = z0 a__add(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__add(z, z') -{ 0 }-> 1 + a__add(mark(z0), mark(z1)) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0 a__add(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__fact(z) -{ 0 }-> a__if(a__zero(a__zero(mark(z01884))), 1 + 0, 1 + (1 + z01884) + (1 + (1 + (1 + z01884)))) :|: z01884 >= 0, z = 1 + z01884 a__fact(z) -{ 0 }-> a__if(a__zero(a__prod(mark(z01885), mark(z1807))), 1 + 0, 1 + (1 + z01885 + z1807) + (1 + (1 + (1 + z01885 + z1807)))) :|: z1807 >= 0, z = 1 + z01885 + z1807, z01885 >= 0 a__fact(z) -{ 0 }-> a__if(a__zero(a__p(mark(z01886))), 1 + 0, 1 + (1 + z01886) + (1 + (1 + (1 + z01886)))) :|: z = 1 + z01886, z01886 >= 0 a__fact(z) -{ 0 }-> a__if(a__zero(a__if(mark(z01883), z1806, z2268)), 1 + 0, 1 + (1 + z01883 + z1806 + z2268) + (1 + (1 + (1 + z01883 + z1806 + z2268)))) :|: z01883 >= 0, z1806 >= 0, z2268 >= 0, z = 1 + z01883 + z1806 + z2268 a__fact(z) -{ 0 }-> a__if(a__zero(a__fact(mark(z01882))), 1 + 0, 1 + (1 + z01882) + (1 + (1 + (1 + z01882)))) :|: z01882 >= 0, z = 1 + z01882 a__fact(z) -{ 0 }-> a__if(a__zero(a__add(mark(z01887), mark(z1808))), 1 + 0, 1 + (1 + z01887 + z1808) + (1 + (1 + (1 + z01887 + z1808)))) :|: z01887 >= 0, z = 1 + z01887 + z1808, z1808 >= 0 a__fact(z) -{ 0 }-> a__if(a__zero(1 + mark(z01888)), 1 + 0, 1 + (1 + z01888) + (1 + (1 + (1 + z01888)))) :|: z = 1 + z01888, z01888 >= 0 a__fact(z) -{ 0 }-> a__if(2, 1 + 0, 1 + z0 + (1 + (1 + z0))) :|: z = z0, z0 >= 0, 0 = 0 a__fact(z) -{ 0 }-> a__if(2, 1 + 0, 1 + 0 + (1 + (1 + 0))) :|: z = 0, 0 = 0 a__fact(z) -{ 0 }-> a__if(1, 1 + 0, 1 + 2 + (1 + (1 + 2))) :|: z = 2, 2 = 1 + z0, z0 >= 0 a__fact(z) -{ 0 }-> a__if(1, 1 + 0, 1 + 1 + (1 + (1 + 1))) :|: z = 1, 1 = 1 + z0, z0 >= 0 a__fact(z) -{ 0 }-> a__if(0, 1 + 0, 1 + z0 + (1 + (1 + z0))) :|: z = z0, z0 >= 0, v0 >= 0, 0 = v0 a__fact(z) -{ 0 }-> a__if(0, 1 + 0, 1 + 2 + (1 + (1 + 2))) :|: z = 2, v0 >= 0, 2 = v0 a__fact(z) -{ 0 }-> a__if(0, 1 + 0, 1 + 1 + (1 + (1 + 1))) :|: z = 1, v0 >= 0, 1 = v0 a__fact(z) -{ 0 }-> a__if(0, 1 + 0, 1 + 0 + (1 + (1 + 0))) :|: z = 0, v0 >= 0, 0 = v0 a__fact(z) -{ 0 }-> a__if(1 + z0, 1 + 0, 1 + 2 + (1 + (1 + 2))) :|: z = 2, 2 = z0, z0 >= 0 a__fact(z) -{ 0 }-> a__if(1 + z0, 1 + 0, 1 + 1 + (1 + (1 + 1))) :|: z = 1, 1 = z0, z0 >= 0 a__fact(z) -{ 0 }-> a__if(1 + z0, 1 + 0, 1 + 0 + (1 + (1 + 0))) :|: z = 0, 0 = z0, z0 >= 0 a__fact(z) -{ 0 }-> a__if(1 + z0', 1 + 0, 1 + z0 + (1 + (1 + z0))) :|: z = z0, z0 >= 0, 0 = z0', z0' >= 0 a__fact(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__fact(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__if(z, z', z'') -{ 0 }-> mark(z0) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1 a__if(z, z', z'') -{ 0 }-> mark(z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 a__if(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 a__if(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 a__p(z) -{ 0 }-> mark(z0) :|: z = 1 + z0, z0 >= 0 a__p(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__p(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__prod(z, z') -{ 0 }-> a__add(mark(z1), a__prod(mark(z0), mark(z1))) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0 a__prod(z, z') -{ 0 }-> 0 :|: z0 >= 0, z = 0, z' = z0 a__prod(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__prod(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__zero(z) -{ 0 }-> 2 :|: z = 0 a__zero(z) -{ 0 }-> 1 :|: z = 1 + z0, z0 >= 0 a__zero(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__zero(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 mark(z) -{ 0 }-> a__zero(a__zero(mark(z02150))) :|: z02150 >= 0, z = 1 + (1 + z02150) mark(z) -{ 0 }-> a__zero(a__prod(mark(z02151), mark(z1921))) :|: z1921 >= 0, z = 1 + (1 + z02151 + z1921), z02151 >= 0 mark(z) -{ 0 }-> a__zero(a__p(mark(z02152))) :|: z = 1 + (1 + z02152), z02152 >= 0 mark(z) -{ 0 }-> a__zero(a__if(mark(z02149), z1920, z2306)) :|: z2306 >= 0, z = 1 + (1 + z02149 + z1920 + z2306), z02149 >= 0, z1920 >= 0 mark(z) -{ 0 }-> a__zero(a__fact(mark(z02148))) :|: z = 1 + (1 + z02148), z02148 >= 0 mark(z) -{ 0 }-> a__zero(a__add(mark(z02153), mark(z1922))) :|: z02153 >= 0, z1922 >= 0, z = 1 + (1 + z02153 + z1922) mark(z) -{ 0 }-> a__zero(1 + mark(z02154)) :|: z02154 >= 0, z = 1 + (1 + z02154) mark(z) -{ 0 }-> a__prod(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__p(a__zero(mark(z02241))) :|: z02241 >= 0, z = 1 + (1 + z02241) mark(z) -{ 0 }-> a__p(a__prod(mark(z02242), mark(z1960))) :|: z02242 >= 0, z = 1 + (1 + z02242 + z1960), z1960 >= 0 mark(z) -{ 0 }-> a__p(a__p(mark(z02243))) :|: z02243 >= 0, z = 1 + (1 + z02243) mark(z) -{ 0 }-> a__p(a__if(mark(z02240), z1959, z2319)) :|: z = 1 + (1 + z02240 + z1959 + z2319), z1959 >= 0, z02240 >= 0, z2319 >= 0 mark(z) -{ 0 }-> a__p(a__fact(mark(z02239))) :|: z02239 >= 0, z = 1 + (1 + z02239) mark(z) -{ 0 }-> a__p(a__add(mark(z02244), mark(z1961))) :|: z1961 >= 0, z02244 >= 0, z = 1 + (1 + z02244 + z1961) mark(z) -{ 0 }-> a__p(2) :|: z = 1 + 2 mark(z) -{ 0 }-> a__p(1) :|: z = 1 + 1 mark(z) -{ 0 }-> a__p(0) :|: z = 1 + 0 mark(z) -{ 0 }-> a__p(0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__p(1 + mark(z02245)) :|: z = 1 + (1 + z02245), z02245 >= 0 mark(z) -{ 0 }-> a__if(a__zero(mark(z02143)), z1, z2) :|: z = 1 + (1 + z02143) + z1 + z2, z1 >= 0, z02143 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__if(a__prod(mark(z02144), mark(z1918)), z1, z2) :|: z = 1 + (1 + z02144 + z1918) + z1 + z2, z1 >= 0, z02144 >= 0, z1918 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__if(a__p(mark(z02145)), z1, z2) :|: z1 >= 0, z02145 >= 0, z = 1 + (1 + z02145) + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__if(a__if(mark(z02142), z1917, z2305), z1, z2) :|: z1 >= 0, z2305 >= 0, z = 1 + (1 + z02142 + z1917 + z2305) + z1 + z2, z02142 >= 0, z2 >= 0, z1917 >= 0 mark(z) -{ 0 }-> a__if(a__fact(mark(z02141)), z1, z2) :|: z1 >= 0, z = 1 + (1 + z02141) + z1 + z2, z2 >= 0, z02141 >= 0 mark(z) -{ 0 }-> a__if(a__add(mark(z02146), mark(z1919)), z1, z2) :|: z = 1 + (1 + z02146 + z1919) + z1 + z2, z1 >= 0, z02146 >= 0, z1919 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__if(2, z1, z2) :|: z1 >= 0, z = 1 + 2 + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__if(1, z1, z2) :|: z1 >= 0, z = 1 + 1 + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__if(0, z1, z2) :|: z1 >= 0, z = 1 + 0 + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__if(0, z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__if(1 + mark(z02147), z1, z2) :|: z02147 >= 0, z1 >= 0, z = 1 + (1 + z02147) + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__fact(a__zero(mark(z02136))) :|: z = 1 + (1 + z02136), z02136 >= 0 mark(z) -{ 0 }-> a__fact(a__prod(mark(z02137), mark(z1915))) :|: z02137 >= 0, z = 1 + (1 + z02137 + z1915), z1915 >= 0 mark(z) -{ 0 }-> a__fact(a__p(mark(z02138))) :|: z = 1 + (1 + z02138), z02138 >= 0 mark(z) -{ 0 }-> a__fact(a__if(mark(z02135), z1914, z2304)) :|: z02135 >= 0, z1914 >= 0, z2304 >= 0, z = 1 + (1 + z02135 + z1914 + z2304) mark(z) -{ 0 }-> a__fact(a__fact(mark(z02134))) :|: z02134 >= 0, z = 1 + (1 + z02134) mark(z) -{ 0 }-> a__fact(a__add(mark(z02139), mark(z1916))) :|: z1916 >= 0, z = 1 + (1 + z02139 + z1916), z02139 >= 0 mark(z) -{ 0 }-> a__fact(2) :|: z = 1 + 2 mark(z) -{ 0 }-> a__fact(1) :|: z = 1 + 1 mark(z) -{ 0 }-> a__fact(0) :|: z = 1 + 0 mark(z) -{ 0 }-> a__fact(0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__fact(1 + mark(z02140)) :|: z = 1 + (1 + z02140), z02140 >= 0 mark(z) -{ 0 }-> a__add(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> 2 :|: z = 2 mark(z) -{ 0 }-> 2 :|: z = 1 + 0, 0 = 0 mark(z) -{ 0 }-> 2 :|: z = 1 + z0, z0 >= 0, 0 = 0 mark(z) -{ 0 }-> 1 :|: z = 1 mark(z) -{ 0 }-> 1 :|: z = 1 + 2, 2 = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> 1 :|: z = 1 + 1, 1 = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> 0 :|: z = 0 mark(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 mark(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0 mark(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 2 = v0 mark(z) -{ 0 }-> 0 :|: z = 1 + 1, v0 >= 0, 1 = v0 mark(z) -{ 0 }-> 0 :|: z = 1 + z0, z0 >= 0, v0 >= 0, 0 = v0 mark(z) -{ 0 }-> 1 + z0 :|: z = 1 + 0, 0 = z0, z0 >= 0 mark(z) -{ 0 }-> 1 + z0 :|: z = 1 + 2, 2 = z0, z0 >= 0 mark(z) -{ 0 }-> 1 + z0 :|: z = 1 + 1, 1 = z0, z0 >= 0 mark(z) -{ 0 }-> 1 + z0' :|: z = 1 + z0, z0 >= 0, 0 = z0', z0' >= 0 mark(z) -{ 0 }-> 1 + mark(z0) :|: z = 1 + z0, z0 >= 0 ---------------------------------------- (63) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (64) Obligation: Complexity RNTS consisting of the following rules: A__ADD(z, z') -{ 1 }-> 1 + MARK(z') :|: z' >= 0, z = 0 A__ADD(z, z') -{ 1 }-> 1 + A__ADD(mark(z - 1), mark(z')) + MARK(z') :|: z' >= 0, z - 1 >= 0 A__ADD(z, z') -{ 1 }-> 1 + A__ADD(mark(z - 1), mark(z')) + MARK(z - 1) :|: z' >= 0, z - 1 >= 0 A__FACT(z) -{ 1 }-> 1 + A__IF(a__zero(a__zero(mark(z - 1))), 1 + 0, 1 + (1 + (z - 1)) + (1 + (1 + (1 + (z - 1))))) + MARK(1 + (z - 1)) :|: z - 1 >= 0 A__FACT(z) -{ 1 }-> 1 + A__IF(a__zero(a__prod(mark(z01878), mark(z1804))), 1 + 0, 1 + (1 + z01878 + z1804) + (1 + (1 + (1 + z01878 + z1804)))) + MARK(1 + z01878 + z1804) :|: z1804 >= 0, z01878 >= 0, z = 1 + z01878 + z1804 A__FACT(z) -{ 1 }-> 1 + A__IF(a__zero(a__p(mark(z - 1))), 1 + 0, 1 + (1 + (z - 1)) + (1 + (1 + (1 + (z - 1))))) + MARK(1 + (z - 1)) :|: z - 1 >= 0 A__FACT(z) -{ 1 }-> 1 + A__IF(a__zero(a__if(mark(z01876), z1803, z2267)), 1 + 0, 1 + (1 + z01876 + z1803 + z2267) + (1 + (1 + (1 + z01876 + z1803 + z2267)))) + MARK(1 + z01876 + z1803 + z2267) :|: z1803 >= 0, z = 1 + z01876 + z1803 + z2267, z2267 >= 0, z01876 >= 0 A__FACT(z) -{ 1 }-> 1 + A__IF(a__zero(a__fact(mark(z - 1))), 1 + 0, 1 + (1 + (z - 1)) + (1 + (1 + (1 + (z - 1))))) + MARK(1 + (z - 1)) :|: z - 1 >= 0 A__FACT(z) -{ 1 }-> 1 + A__IF(a__zero(a__add(mark(z01880), mark(z1805))), 1 + 0, 1 + (1 + z01880 + z1805) + (1 + (1 + (1 + z01880 + z1805)))) + MARK(1 + z01880 + z1805) :|: z01880 >= 0, z = 1 + z01880 + z1805, z1805 >= 0 A__FACT(z) -{ 1 }-> 1 + A__IF(a__zero(1 + mark(z - 1)), 1 + 0, 1 + (1 + (z - 1)) + (1 + (1 + (1 + (z - 1))))) + MARK(1 + (z - 1)) :|: z - 1 >= 0 A__FACT(z) -{ 1 }-> 1 + A__IF(2, 1 + 0, 1 + z + (1 + (1 + z))) + MARK(z) :|: z >= 0, 0 = 0 A__FACT(z) -{ 1 }-> 1 + A__IF(2, 1 + 0, 1 + 0 + (1 + (1 + 0))) + MARK(0) :|: z = 0, 0 = 0 A__FACT(z) -{ 1 }-> 1 + A__IF(1, 1 + 0, 1 + 2 + (1 + (1 + 2))) + MARK(2) :|: z = 2, 2 = 1 + z0, z0 >= 0 A__FACT(z) -{ 1 }-> 1 + A__IF(1, 1 + 0, 1 + 1 + (1 + (1 + 1))) + MARK(1) :|: z = 1, 1 = 1 + z0, z0 >= 0 A__FACT(z) -{ 1 }-> 1 + A__IF(0, 1 + 0, 1 + z + (1 + (1 + z))) + MARK(z) :|: z >= 0, v0 >= 0, 0 = v0 A__FACT(z) -{ 1 }-> 1 + A__IF(0, 1 + 0, 1 + 2 + (1 + (1 + 2))) + MARK(2) :|: z = 2, v0 >= 0, 2 = v0 A__FACT(z) -{ 1 }-> 1 + A__IF(0, 1 + 0, 1 + 1 + (1 + (1 + 1))) + MARK(1) :|: z = 1, v0 >= 0, 1 = v0 A__FACT(z) -{ 1 }-> 1 + A__IF(0, 1 + 0, 1 + 0 + (1 + (1 + 0))) + MARK(0) :|: z = 0, v0 >= 0, 0 = v0 A__FACT(z) -{ 1 }-> 1 + A__IF(1 + z0, 1 + 0, 1 + 2 + (1 + (1 + 2))) + MARK(2) :|: z = 2, 2 = z0, z0 >= 0 A__FACT(z) -{ 1 }-> 1 + A__IF(1 + z0, 1 + 0, 1 + 1 + (1 + (1 + 1))) + MARK(1) :|: z = 1, 1 = z0, z0 >= 0 A__FACT(z) -{ 1 }-> 1 + A__IF(1 + z0, 1 + 0, 1 + 0 + (1 + (1 + 0))) + MARK(0) :|: z = 0, 0 = z0, z0 >= 0 A__FACT(z) -{ 1 }-> 1 + A__IF(1 + z0', 1 + 0, 1 + z + (1 + (1 + z))) + MARK(z) :|: z >= 0, 0 = z0', z0' >= 0 A__IF(z, z', z'') -{ 1 }-> 1 + MARK(z') :|: z = 2, z'' >= 0, z' >= 0 A__IF(z, z', z'') -{ 1 }-> 1 + MARK(z'') :|: z'' >= 0, z = 1, z' >= 0 A__P(z) -{ 1 }-> 1 + MARK(z - 1) :|: z - 1 >= 0 A__PROD(z, z') -{ 1 }-> 1 + A__ADD(mark(z'), a__prod(mark(z - 1), mark(z'))) + MARK(z') :|: z' >= 0, z - 1 >= 0 A__PROD(z, z') -{ 1 }-> 1 + A__ADD(mark(z'), a__prod(mark(z - 1), mark(z'))) + A__PROD(mark(z - 1), mark(z')) + MARK(z') :|: z' >= 0, z - 1 >= 0 A__PROD(z, z') -{ 1 }-> 1 + A__ADD(mark(z'), a__prod(mark(z - 1), mark(z'))) + A__PROD(mark(z - 1), mark(z')) + MARK(z - 1) :|: z' >= 0, z - 1 >= 0 MARK(z) -{ 1 }-> 1 + MARK(z - 1) :|: z - 1 >= 0 MARK(z) -{ 1 }-> 1 + A__PROD(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__PROD(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__P(a__zero(mark(z - 2))) + MARK(1 + (z - 2)) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__P(a__prod(mark(z01703), mark(z1729))) + MARK(1 + z01703 + z1729) :|: z1729 >= 0, z = 1 + (1 + z01703 + z1729), z01703 >= 0 MARK(z) -{ 1 }-> 1 + A__P(a__p(mark(z - 2))) + MARK(1 + (z - 2)) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__P(a__if(mark(z01701), z1728, z2242)) + MARK(1 + z01701 + z1728 + z2242) :|: z = 1 + (1 + z01701 + z1728 + z2242), z01701 >= 0, z1728 >= 0, z2242 >= 0 MARK(z) -{ 1 }-> 1 + A__P(a__fact(mark(z - 2))) + MARK(1 + (z - 2)) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__P(a__add(mark(z01705), mark(z1730))) + MARK(1 + z01705 + z1730) :|: z01705 >= 0, z = 1 + (1 + z01705 + z1730), z1730 >= 0 MARK(z) -{ 1 }-> 1 + A__P(2) + MARK(2) :|: z = 1 + 2 MARK(z) -{ 1 }-> 1 + A__P(1) + MARK(1) :|: z = 1 + 1 MARK(z) -{ 1 }-> 1 + A__P(0) + MARK(0) :|: z = 1 + 0 MARK(z) -{ 1 }-> 1 + A__P(0) + MARK(z - 1) :|: z - 1 >= 0 MARK(z) -{ 1 }-> 1 + A__P(1 + mark(z - 2)) + MARK(1 + (z - 2)) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__IF(a__zero(mark(z01527)), z1, z2) + MARK(1 + z01527) :|: z1 >= 0, z01527 >= 0, z = 1 + (1 + z01527) + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__IF(a__prod(mark(z01528), mark(z1654)), z1, z2) + MARK(1 + z01528 + z1654) :|: z01528 >= 0, z1654 >= 0, z1 >= 0, z = 1 + (1 + z01528 + z1654) + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__IF(a__p(mark(z01529)), z1, z2) + MARK(1 + z01529) :|: z1 >= 0, z = 1 + (1 + z01529) + z1 + z2, z2 >= 0, z01529 >= 0 MARK(z) -{ 1 }-> 1 + A__IF(a__if(mark(z01526), z1653, z2217), z1, z2) + MARK(1 + z01526 + z1653 + z2217) :|: z = 1 + (1 + z01526 + z1653 + z2217) + z1 + z2, z1 >= 0, z2217 >= 0, z01526 >= 0, z1653 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__IF(a__fact(mark(z01525)), z1, z2) + MARK(1 + z01525) :|: z = 1 + (1 + z01525) + z1 + z2, z1 >= 0, z01525 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__IF(a__add(mark(z01530), mark(z1655)), z1, z2) + MARK(1 + z01530 + z1655) :|: z01530 >= 0, z1 >= 0, z = 1 + (1 + z01530 + z1655) + z1 + z2, z1655 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__IF(2, z1, z2) + MARK(2) :|: z1 >= 0, z = 1 + 2 + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__IF(1, z1, z2) + MARK(1) :|: z1 >= 0, z = 1 + 1 + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__IF(0, z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__IF(0, z1, z2) + MARK(0) :|: z1 >= 0, z = 1 + 0 + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__IF(1 + mark(z01531), z1, z2) + MARK(1 + z01531) :|: z1 >= 0, z = 1 + (1 + z01531) + z1 + z2, z2 >= 0, z01531 >= 0 MARK(z) -{ 1 }-> 1 + A__FACT(a__zero(mark(z - 2))) + MARK(1 + (z - 2)) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__FACT(a__prod(mark(z01521), mark(z1651))) + MARK(1 + z01521 + z1651) :|: z1651 >= 0, z = 1 + (1 + z01521 + z1651), z01521 >= 0 MARK(z) -{ 1 }-> 1 + A__FACT(a__p(mark(z - 2))) + MARK(1 + (z - 2)) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__FACT(a__if(mark(z01519), z1650, z2216)) + MARK(1 + z01519 + z1650 + z2216) :|: z1650 >= 0, z2216 >= 0, z = 1 + (1 + z01519 + z1650 + z2216), z01519 >= 0 MARK(z) -{ 1 }-> 1 + A__FACT(a__fact(mark(z - 2))) + MARK(1 + (z - 2)) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__FACT(a__add(mark(z01523), mark(z1652))) + MARK(1 + z01523 + z1652) :|: z = 1 + (1 + z01523 + z1652), z01523 >= 0, z1652 >= 0 MARK(z) -{ 1 }-> 1 + A__FACT(2) + MARK(2) :|: z = 1 + 2 MARK(z) -{ 1 }-> 1 + A__FACT(1) + MARK(1) :|: z = 1 + 1 MARK(z) -{ 1 }-> 1 + A__FACT(0) + MARK(0) :|: z = 1 + 0 MARK(z) -{ 1 }-> 1 + A__FACT(0) + MARK(z - 1) :|: z - 1 >= 0 MARK(z) -{ 1 }-> 1 + A__FACT(1 + mark(z - 2)) + MARK(1 + (z - 2)) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__ADD(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__ADD(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__add(z, z') -{ 0 }-> mark(z') :|: z' >= 0, z = 0 a__add(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 a__add(z, z') -{ 0 }-> 1 + a__add(mark(z - 1), mark(z')) :|: z' >= 0, z - 1 >= 0 a__add(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 a__fact(z) -{ 0 }-> a__if(a__zero(a__zero(mark(z - 1))), 1 + 0, 1 + (1 + (z - 1)) + (1 + (1 + (1 + (z - 1))))) :|: z - 1 >= 0 a__fact(z) -{ 0 }-> a__if(a__zero(a__prod(mark(z01885), mark(z1807))), 1 + 0, 1 + (1 + z01885 + z1807) + (1 + (1 + (1 + z01885 + z1807)))) :|: z1807 >= 0, z = 1 + z01885 + z1807, z01885 >= 0 a__fact(z) -{ 0 }-> a__if(a__zero(a__p(mark(z - 1))), 1 + 0, 1 + (1 + (z - 1)) + (1 + (1 + (1 + (z - 1))))) :|: z - 1 >= 0 a__fact(z) -{ 0 }-> a__if(a__zero(a__if(mark(z01883), z1806, z2268)), 1 + 0, 1 + (1 + z01883 + z1806 + z2268) + (1 + (1 + (1 + z01883 + z1806 + z2268)))) :|: z01883 >= 0, z1806 >= 0, z2268 >= 0, z = 1 + z01883 + z1806 + z2268 a__fact(z) -{ 0 }-> a__if(a__zero(a__fact(mark(z - 1))), 1 + 0, 1 + (1 + (z - 1)) + (1 + (1 + (1 + (z - 1))))) :|: z - 1 >= 0 a__fact(z) -{ 0 }-> a__if(a__zero(a__add(mark(z01887), mark(z1808))), 1 + 0, 1 + (1 + z01887 + z1808) + (1 + (1 + (1 + z01887 + z1808)))) :|: z01887 >= 0, z = 1 + z01887 + z1808, z1808 >= 0 a__fact(z) -{ 0 }-> a__if(a__zero(1 + mark(z - 1)), 1 + 0, 1 + (1 + (z - 1)) + (1 + (1 + (1 + (z - 1))))) :|: z - 1 >= 0 a__fact(z) -{ 0 }-> a__if(2, 1 + 0, 1 + z + (1 + (1 + z))) :|: z >= 0, 0 = 0 a__fact(z) -{ 0 }-> a__if(2, 1 + 0, 1 + 0 + (1 + (1 + 0))) :|: z = 0, 0 = 0 a__fact(z) -{ 0 }-> a__if(1, 1 + 0, 1 + 2 + (1 + (1 + 2))) :|: z = 2, 2 = 1 + z0, z0 >= 0 a__fact(z) -{ 0 }-> a__if(1, 1 + 0, 1 + 1 + (1 + (1 + 1))) :|: z = 1, 1 = 1 + z0, z0 >= 0 a__fact(z) -{ 0 }-> a__if(0, 1 + 0, 1 + z + (1 + (1 + z))) :|: z >= 0, v0 >= 0, 0 = v0 a__fact(z) -{ 0 }-> a__if(0, 1 + 0, 1 + 2 + (1 + (1 + 2))) :|: z = 2, v0 >= 0, 2 = v0 a__fact(z) -{ 0 }-> a__if(0, 1 + 0, 1 + 1 + (1 + (1 + 1))) :|: z = 1, v0 >= 0, 1 = v0 a__fact(z) -{ 0 }-> a__if(0, 1 + 0, 1 + 0 + (1 + (1 + 0))) :|: z = 0, v0 >= 0, 0 = v0 a__fact(z) -{ 0 }-> a__if(1 + z0, 1 + 0, 1 + 2 + (1 + (1 + 2))) :|: z = 2, 2 = z0, z0 >= 0 a__fact(z) -{ 0 }-> a__if(1 + z0, 1 + 0, 1 + 1 + (1 + (1 + 1))) :|: z = 1, 1 = z0, z0 >= 0 a__fact(z) -{ 0 }-> a__if(1 + z0, 1 + 0, 1 + 0 + (1 + (1 + 0))) :|: z = 0, 0 = z0, z0 >= 0 a__fact(z) -{ 0 }-> a__if(1 + z0', 1 + 0, 1 + z + (1 + (1 + z))) :|: z >= 0, 0 = z0', z0' >= 0 a__fact(z) -{ 0 }-> 0 :|: z >= 0 a__fact(z) -{ 0 }-> 1 + z :|: z >= 0 a__if(z, z', z'') -{ 0 }-> mark(z') :|: z = 2, z'' >= 0, z' >= 0 a__if(z, z', z'') -{ 0 }-> mark(z'') :|: z'' >= 0, z = 1, z' >= 0 a__if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 a__if(z, z', z'') -{ 0 }-> 1 + z + z' + z'' :|: z' >= 0, z >= 0, z'' >= 0 a__p(z) -{ 0 }-> mark(z - 1) :|: z - 1 >= 0 a__p(z) -{ 0 }-> 0 :|: z >= 0 a__p(z) -{ 0 }-> 1 + z :|: z >= 0 a__prod(z, z') -{ 0 }-> a__add(mark(z'), a__prod(mark(z - 1), mark(z'))) :|: z' >= 0, z - 1 >= 0 a__prod(z, z') -{ 0 }-> 0 :|: z' >= 0, z = 0 a__prod(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 a__prod(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 a__zero(z) -{ 0 }-> 2 :|: z = 0 a__zero(z) -{ 0 }-> 1 :|: z - 1 >= 0 a__zero(z) -{ 0 }-> 0 :|: z >= 0 a__zero(z) -{ 0 }-> 1 + z :|: z >= 0 mark(z) -{ 0 }-> a__zero(a__zero(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__zero(a__prod(mark(z02151), mark(z1921))) :|: z1921 >= 0, z = 1 + (1 + z02151 + z1921), z02151 >= 0 mark(z) -{ 0 }-> a__zero(a__p(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__zero(a__if(mark(z02149), z1920, z2306)) :|: z2306 >= 0, z = 1 + (1 + z02149 + z1920 + z2306), z02149 >= 0, z1920 >= 0 mark(z) -{ 0 }-> a__zero(a__fact(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__zero(a__add(mark(z02153), mark(z1922))) :|: z02153 >= 0, z1922 >= 0, z = 1 + (1 + z02153 + z1922) mark(z) -{ 0 }-> a__zero(1 + mark(z - 2)) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__prod(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__p(a__zero(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__p(a__prod(mark(z02242), mark(z1960))) :|: z02242 >= 0, z = 1 + (1 + z02242 + z1960), z1960 >= 0 mark(z) -{ 0 }-> a__p(a__p(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__p(a__if(mark(z02240), z1959, z2319)) :|: z = 1 + (1 + z02240 + z1959 + z2319), z1959 >= 0, z02240 >= 0, z2319 >= 0 mark(z) -{ 0 }-> a__p(a__fact(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__p(a__add(mark(z02244), mark(z1961))) :|: z1961 >= 0, z02244 >= 0, z = 1 + (1 + z02244 + z1961) mark(z) -{ 0 }-> a__p(2) :|: z = 1 + 2 mark(z) -{ 0 }-> a__p(1) :|: z = 1 + 1 mark(z) -{ 0 }-> a__p(0) :|: z = 1 + 0 mark(z) -{ 0 }-> a__p(0) :|: z - 1 >= 0 mark(z) -{ 0 }-> a__p(1 + mark(z - 2)) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__if(a__zero(mark(z02143)), z1, z2) :|: z = 1 + (1 + z02143) + z1 + z2, z1 >= 0, z02143 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__if(a__prod(mark(z02144), mark(z1918)), z1, z2) :|: z = 1 + (1 + z02144 + z1918) + z1 + z2, z1 >= 0, z02144 >= 0, z1918 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__if(a__p(mark(z02145)), z1, z2) :|: z1 >= 0, z02145 >= 0, z = 1 + (1 + z02145) + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__if(a__if(mark(z02142), z1917, z2305), z1, z2) :|: z1 >= 0, z2305 >= 0, z = 1 + (1 + z02142 + z1917 + z2305) + z1 + z2, z02142 >= 0, z2 >= 0, z1917 >= 0 mark(z) -{ 0 }-> a__if(a__fact(mark(z02141)), z1, z2) :|: z1 >= 0, z = 1 + (1 + z02141) + z1 + z2, z2 >= 0, z02141 >= 0 mark(z) -{ 0 }-> a__if(a__add(mark(z02146), mark(z1919)), z1, z2) :|: z = 1 + (1 + z02146 + z1919) + z1 + z2, z1 >= 0, z02146 >= 0, z1919 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__if(2, z1, z2) :|: z1 >= 0, z = 1 + 2 + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__if(1, z1, z2) :|: z1 >= 0, z = 1 + 1 + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__if(0, z1, z2) :|: z1 >= 0, z = 1 + 0 + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__if(0, z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__if(1 + mark(z02147), z1, z2) :|: z02147 >= 0, z1 >= 0, z = 1 + (1 + z02147) + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__fact(a__zero(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__fact(a__prod(mark(z02137), mark(z1915))) :|: z02137 >= 0, z = 1 + (1 + z02137 + z1915), z1915 >= 0 mark(z) -{ 0 }-> a__fact(a__p(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__fact(a__if(mark(z02135), z1914, z2304)) :|: z02135 >= 0, z1914 >= 0, z2304 >= 0, z = 1 + (1 + z02135 + z1914 + z2304) mark(z) -{ 0 }-> a__fact(a__fact(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__fact(a__add(mark(z02139), mark(z1916))) :|: z1916 >= 0, z = 1 + (1 + z02139 + z1916), z02139 >= 0 mark(z) -{ 0 }-> a__fact(2) :|: z = 1 + 2 mark(z) -{ 0 }-> a__fact(1) :|: z = 1 + 1 mark(z) -{ 0 }-> a__fact(0) :|: z = 1 + 0 mark(z) -{ 0 }-> a__fact(0) :|: z - 1 >= 0 mark(z) -{ 0 }-> a__fact(1 + mark(z - 2)) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__add(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> 2 :|: z = 2 mark(z) -{ 0 }-> 2 :|: z = 1 + 0, 0 = 0 mark(z) -{ 0 }-> 2 :|: z - 1 >= 0, 0 = 0 mark(z) -{ 0 }-> 1 :|: z = 1 mark(z) -{ 0 }-> 1 :|: z = 1 + 2, 2 = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> 1 :|: z = 1 + 1, 1 = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> 0 :|: z = 0 mark(z) -{ 0 }-> 0 :|: z >= 0 mark(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0 mark(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 2 = v0 mark(z) -{ 0 }-> 0 :|: z = 1 + 1, v0 >= 0, 1 = v0 mark(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0 mark(z) -{ 0 }-> 1 + z0 :|: z = 1 + 0, 0 = z0, z0 >= 0 mark(z) -{ 0 }-> 1 + z0 :|: z = 1 + 2, 2 = z0, z0 >= 0 mark(z) -{ 0 }-> 1 + z0 :|: z = 1 + 1, 1 = z0, z0 >= 0 mark(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, 0 = z0', z0' >= 0 mark(z) -{ 0 }-> 1 + mark(z - 1) :|: z - 1 >= 0 ---------------------------------------- (65) 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__fact(v0) -> null_a__fact [0] a__add(v0, v1) -> null_a__add [0] a__prod(v0, v1) -> null_a__prod [0] a__if(v0, v1, v2) -> null_a__if [0] a__zero(v0) -> null_a__zero [0] a__p(v0) -> null_a__p [0] mark(v0) -> null_mark [0] A__ADD(v0, v1) -> null_A__ADD [0] A__PROD(v0, v1) -> null_A__PROD [0] A__IF(v0, v1, v2) -> null_A__IF [0] A__P(v0) -> null_A__P [0] MARK(v0) -> null_MARK [0] And the following fresh constants: null_a__fact, null_a__add, null_a__prod, null_a__if, null_a__zero, null_a__p, null_mark, null_A__ADD, null_A__PROD, null_A__IF, null_A__P, null_MARK, const ---------------------------------------- (66) 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__ADD(0, z0) -> c2(MARK(z0)) [1] A__ADD(s(z0), z1) -> c3(A__ADD(mark(z0), mark(z1)), MARK(z0)) [1] A__ADD(s(z0), z1) -> c4(A__ADD(mark(z0), mark(z1)), MARK(z1)) [1] A__PROD(s(z0), z1) -> c7(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), MARK(z1)) [1] A__PROD(s(z0), z1) -> c8(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z0)) [1] A__PROD(s(z0), z1) -> c9(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z1)) [1] A__IF(true, z0, z1) -> c11(MARK(z0)) [1] A__IF(false, z0, z1) -> c12(MARK(z1)) [1] A__P(s(z0)) -> c17(MARK(z0)) [1] MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) [1] MARK(if(z0, z1, z2)) -> c20(A__IF(mark(z0), z1, z2), MARK(z0)) [1] MARK(prod(z0, z1)) -> c22(A__PROD(mark(z0), mark(z1)), MARK(z0)) [1] MARK(prod(z0, z1)) -> c23(A__PROD(mark(z0), mark(z1)), MARK(z1)) [1] MARK(p(z0)) -> c24(A__P(mark(z0)), MARK(z0)) [1] MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) [1] MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) [1] MARK(s(z0)) -> c27(MARK(z0)) [1] A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), MARK(z0)) [1] MARK(zero(z0)) -> c21(MARK(z0)) [1] a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) [0] a__fact(z0) -> fact(z0) [0] a__add(0, z0) -> mark(z0) [0] a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) [0] a__add(z0, z1) -> add(z0, z1) [0] a__prod(0, z0) -> 0 [0] a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) [0] a__prod(z0, z1) -> prod(z0, z1) [0] a__if(true, z0, z1) -> mark(z0) [0] a__if(false, z0, z1) -> mark(z1) [0] a__if(z0, z1, z2) -> if(z0, z1, z2) [0] a__zero(0) -> true [0] a__zero(s(z0)) -> false [0] a__zero(z0) -> zero(z0) [0] a__p(s(z0)) -> mark(z0) [0] a__p(z0) -> p(z0) [0] mark(fact(z0)) -> a__fact(mark(z0)) [0] mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) [0] mark(zero(z0)) -> a__zero(mark(z0)) [0] mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) [0] mark(p(z0)) -> a__p(mark(z0)) [0] mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) [0] mark(s(z0)) -> s(mark(z0)) [0] mark(0) -> 0 [0] mark(true) -> true [0] mark(false) -> false [0] a__fact(v0) -> null_a__fact [0] a__add(v0, v1) -> null_a__add [0] a__prod(v0, v1) -> null_a__prod [0] a__if(v0, v1, v2) -> null_a__if [0] a__zero(v0) -> null_a__zero [0] a__p(v0) -> null_a__p [0] mark(v0) -> null_mark [0] A__ADD(v0, v1) -> null_A__ADD [0] A__PROD(v0, v1) -> null_A__PROD [0] A__IF(v0, v1, v2) -> null_A__IF [0] A__P(v0) -> null_A__P [0] MARK(v0) -> null_MARK [0] The TRS has the following type information: A__ADD :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> c2:c3:c4:null_A__ADD 0 :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark c2 :: c19:c20:c22:c23:c24:c25:c26:c27:c21:null_MARK -> c2:c3:c4:null_A__ADD MARK :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> c19:c20:c22:c23:c24:c25:c26:c27:c21:null_MARK s :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark c3 :: c2:c3:c4:null_A__ADD -> c19:c20:c22:c23:c24:c25:c26:c27:c21:null_MARK -> c2:c3:c4:null_A__ADD mark :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark c4 :: c2:c3:c4:null_A__ADD -> c19:c20:c22:c23:c24:c25:c26:c27:c21:null_MARK -> c2:c3:c4:null_A__ADD A__PROD :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> c7:c8:c9:null_A__PROD c7 :: c2:c3:c4:null_A__ADD -> c19:c20:c22:c23:c24:c25:c26:c27:c21:null_MARK -> c7:c8:c9:null_A__PROD a__prod :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark c8 :: c2:c3:c4:null_A__ADD -> c7:c8:c9:null_A__PROD -> c19:c20:c22:c23:c24:c25:c26:c27:c21:null_MARK -> c7:c8:c9:null_A__PROD c9 :: c2:c3:c4:null_A__ADD -> c7:c8:c9:null_A__PROD -> c19:c20:c22:c23:c24:c25:c26:c27:c21:null_MARK -> c7:c8:c9:null_A__PROD A__IF :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> c11:c12:null_A__IF true :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark c11 :: c19:c20:c22:c23:c24:c25:c26:c27:c21:null_MARK -> c11:c12:null_A__IF false :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark c12 :: c19:c20:c22:c23:c24:c25:c26:c27:c21:null_MARK -> c11:c12:null_A__IF A__P :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> c17:null_A__P c17 :: c19:c20:c22:c23:c24:c25:c26:c27:c21:null_MARK -> c17:null_A__P fact :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark c19 :: c -> c19:c20:c22:c23:c24:c25:c26:c27:c21:null_MARK -> c19:c20:c22:c23:c24:c25:c26:c27:c21:null_MARK A__FACT :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> c if :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark c20 :: c11:c12:null_A__IF -> c19:c20:c22:c23:c24:c25:c26:c27:c21:null_MARK -> c19:c20:c22:c23:c24:c25:c26:c27:c21:null_MARK prod :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark c22 :: c7:c8:c9:null_A__PROD -> c19:c20:c22:c23:c24:c25:c26:c27:c21:null_MARK -> c19:c20:c22:c23:c24:c25:c26:c27:c21:null_MARK c23 :: c7:c8:c9:null_A__PROD -> c19:c20:c22:c23:c24:c25:c26:c27:c21:null_MARK -> c19:c20:c22:c23:c24:c25:c26:c27:c21:null_MARK p :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark c24 :: c17:null_A__P -> c19:c20:c22:c23:c24:c25:c26:c27:c21:null_MARK -> c19:c20:c22:c23:c24:c25:c26:c27:c21:null_MARK add :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark c25 :: c2:c3:c4:null_A__ADD -> c19:c20:c22:c23:c24:c25:c26:c27:c21:null_MARK -> c19:c20:c22:c23:c24:c25:c26:c27:c21:null_MARK c26 :: c2:c3:c4:null_A__ADD -> c19:c20:c22:c23:c24:c25:c26:c27:c21:null_MARK -> c19:c20:c22:c23:c24:c25:c26:c27:c21:null_MARK c27 :: c19:c20:c22:c23:c24:c25:c26:c27:c21:null_MARK -> c19:c20:c22:c23:c24:c25:c26:c27:c21:null_MARK c :: c11:c12:null_A__IF -> c19:c20:c22:c23:c24:c25:c26:c27:c21:null_MARK -> c a__zero :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark zero :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark c21 :: c19:c20:c22:c23:c24:c25:c26:c27:c21:null_MARK -> c19:c20:c22:c23:c24:c25:c26:c27:c21:null_MARK a__fact :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark a__if :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark a__add :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark a__p :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark -> 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark null_a__fact :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark null_a__add :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark null_a__prod :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark null_a__if :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark null_a__zero :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark null_a__p :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark null_mark :: 0:s:true:false:fact:if:prod:p:add:zero:null_a__fact:null_a__add:null_a__prod:null_a__if:null_a__zero:null_a__p:null_mark null_A__ADD :: c2:c3:c4:null_A__ADD null_A__PROD :: c7:c8:c9:null_A__PROD null_A__IF :: c11:c12:null_A__IF null_A__P :: c17:null_A__P null_MARK :: c19:c20:c22:c23:c24:c25:c26:c27:c21:null_MARK const :: c Rewrite Strategy: INNERMOST ---------------------------------------- (67) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: 0 => 0 true => 2 false => 1 null_a__fact => 0 null_a__add => 0 null_a__prod => 0 null_a__if => 0 null_a__zero => 0 null_a__p => 0 null_mark => 0 null_A__ADD => 0 null_A__PROD => 0 null_A__IF => 0 null_A__P => 0 null_MARK => 0 const => 0 ---------------------------------------- (68) Obligation: Complexity RNTS consisting of the following rules: A__ADD(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 A__ADD(z, z') -{ 1 }-> 1 + MARK(z0) :|: z0 >= 0, z = 0, z' = z0 A__ADD(z, z') -{ 1 }-> 1 + A__ADD(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0 A__ADD(z, z') -{ 1 }-> 1 + A__ADD(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0 A__FACT(z) -{ 1 }-> 1 + A__IF(a__zero(mark(z0)), 1 + 0, 1 + z0 + (1 + (1 + z0))) + MARK(z0) :|: z = z0, z0 >= 0 A__IF(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 A__IF(z, z', z'') -{ 1 }-> 1 + MARK(z0) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1 A__IF(z, z', z'') -{ 1 }-> 1 + MARK(z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 A__P(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 A__P(z) -{ 1 }-> 1 + MARK(z0) :|: z = 1 + z0, z0 >= 0 A__PROD(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 A__PROD(z, z') -{ 1 }-> 1 + A__ADD(mark(z1), a__prod(mark(z0), mark(z1))) + MARK(z1) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0 A__PROD(z, z') -{ 1 }-> 1 + A__ADD(mark(z1), a__prod(mark(z0), mark(z1))) + A__PROD(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0 A__PROD(z, z') -{ 1 }-> 1 + A__ADD(mark(z1), a__prod(mark(z0), mark(z1))) + A__PROD(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0 MARK(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__PROD(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__PROD(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__P(mark(z0)) + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__IF(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__FACT(mark(z0)) + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__ADD(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__ADD(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__add(z, z') -{ 0 }-> mark(z0) :|: z0 >= 0, z = 0, z' = z0 a__add(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__add(z, z') -{ 0 }-> 1 + a__add(mark(z0), mark(z1)) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0 a__add(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__fact(z) -{ 0 }-> a__if(a__zero(mark(z0)), 1 + 0, 1 + z0 + (1 + (1 + z0))) :|: z = z0, z0 >= 0 a__fact(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__fact(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__if(z, z', z'') -{ 0 }-> mark(z0) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1 a__if(z, z', z'') -{ 0 }-> mark(z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 a__if(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 a__if(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 a__p(z) -{ 0 }-> mark(z0) :|: z = 1 + z0, z0 >= 0 a__p(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__p(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__prod(z, z') -{ 0 }-> a__add(mark(z1), a__prod(mark(z0), mark(z1))) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0 a__prod(z, z') -{ 0 }-> 0 :|: z0 >= 0, z = 0, z' = z0 a__prod(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__prod(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__zero(z) -{ 0 }-> 2 :|: z = 0 a__zero(z) -{ 0 }-> 1 :|: z = 1 + z0, z0 >= 0 a__zero(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__zero(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 mark(z) -{ 0 }-> a__zero(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__prod(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__p(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__if(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__fact(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__add(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> 2 :|: z = 2 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. ---------------------------------------- (69) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__ADD(s(z0), z1) -> c3(A__ADD(mark(z0), mark(z1)), MARK(z0)) by A__ADD(s(x0), fact(z0)) -> c3(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) A__ADD(s(x0), if(z0, z1, z2)) -> c3(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1)), MARK(0)) A__ADD(s(true), x1) -> c3(A__ADD(true, mark(x1)), MARK(true)) A__ADD(s(false), x1) -> c3(A__ADD(false, mark(x1)), MARK(false)) ---------------------------------------- (70) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__ADD(s(z0), z1) -> c4(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__PROD(s(z0), z1) -> c7(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), MARK(z1)) A__PROD(s(z0), z1) -> c8(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z0)) A__PROD(s(z0), z1) -> c9(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z1)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(if(z0, z1, z2)) -> c20(A__IF(mark(z0), z1, z2), MARK(z0)) MARK(prod(z0, z1)) -> c22(A__PROD(mark(z0), mark(z1)), MARK(z0)) MARK(prod(z0, z1)) -> c23(A__PROD(mark(z0), mark(z1)), MARK(z1)) MARK(p(z0)) -> c24(A__P(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), fact(z0)) -> c3(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) A__ADD(s(x0), if(z0, z1, z2)) -> c3(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1)), MARK(0)) A__ADD(s(true), x1) -> c3(A__ADD(true, mark(x1)), MARK(true)) A__ADD(s(false), x1) -> c3(A__ADD(false, mark(x1)), MARK(false)) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__ADD(s(z0), z1) -> c4(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__PROD(s(z0), z1) -> c7(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), MARK(z1)) A__PROD(s(z0), z1) -> c8(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z0)) A__PROD(s(z0), z1) -> c9(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z1)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(if(z0, z1, z2)) -> c20(A__IF(mark(z0), z1, z2), MARK(z0)) MARK(prod(z0, z1)) -> c22(A__PROD(mark(z0), mark(z1)), MARK(z0)) MARK(prod(z0, z1)) -> c23(A__PROD(mark(z0), mark(z1)), MARK(z1)) MARK(p(z0)) -> c24(A__P(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), fact(z0)) -> c3(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) A__ADD(s(x0), if(z0, z1, z2)) -> c3(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1)), MARK(0)) A__ADD(s(true), x1) -> c3(A__ADD(true, mark(x1)), MARK(true)) A__ADD(s(false), x1) -> c3(A__ADD(false, mark(x1)), MARK(false)) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__PROD_2, A__IF_3, A__P_1, MARK_1, A__FACT_1 Compound Symbols: c2_1, c4_2, c7_2, c8_3, c9_3, c11_1, c12_1, c17_1, c19_2, c20_2, c22_2, c23_2, c24_2, c25_2, c26_2, c27_1, c_2, c21_1, c3_2 ---------------------------------------- (71) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: A__ADD(s(true), x1) -> c3(A__ADD(true, mark(x1)), MARK(true)) A__ADD(s(false), x1) -> c3(A__ADD(false, mark(x1)), MARK(false)) ---------------------------------------- (72) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__ADD(s(z0), z1) -> c4(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__PROD(s(z0), z1) -> c7(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), MARK(z1)) A__PROD(s(z0), z1) -> c8(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z0)) A__PROD(s(z0), z1) -> c9(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z1)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(if(z0, z1, z2)) -> c20(A__IF(mark(z0), z1, z2), MARK(z0)) MARK(prod(z0, z1)) -> c22(A__PROD(mark(z0), mark(z1)), MARK(z0)) MARK(prod(z0, z1)) -> c23(A__PROD(mark(z0), mark(z1)), MARK(z1)) MARK(p(z0)) -> c24(A__P(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), fact(z0)) -> c3(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) A__ADD(s(x0), if(z0, z1, z2)) -> c3(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1)), MARK(0)) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__ADD(s(z0), z1) -> c4(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__PROD(s(z0), z1) -> c7(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), MARK(z1)) A__PROD(s(z0), z1) -> c8(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z0)) A__PROD(s(z0), z1) -> c9(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z1)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(if(z0, z1, z2)) -> c20(A__IF(mark(z0), z1, z2), MARK(z0)) MARK(prod(z0, z1)) -> c22(A__PROD(mark(z0), mark(z1)), MARK(z0)) MARK(prod(z0, z1)) -> c23(A__PROD(mark(z0), mark(z1)), MARK(z1)) MARK(p(z0)) -> c24(A__P(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), fact(z0)) -> c3(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) A__ADD(s(x0), if(z0, z1, z2)) -> c3(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1)), MARK(0)) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__PROD_2, A__IF_3, A__P_1, MARK_1, A__FACT_1 Compound Symbols: c2_1, c4_2, c7_2, c8_3, c9_3, c11_1, c12_1, c17_1, c19_2, c20_2, c22_2, c23_2, c24_2, c25_2, c26_2, c27_1, c_2, c21_1, c3_2 ---------------------------------------- (73) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (74) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__ADD(s(z0), z1) -> c4(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__PROD(s(z0), z1) -> c7(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), MARK(z1)) A__PROD(s(z0), z1) -> c8(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z0)) A__PROD(s(z0), z1) -> c9(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z1)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(if(z0, z1, z2)) -> c20(A__IF(mark(z0), z1, z2), MARK(z0)) MARK(prod(z0, z1)) -> c22(A__PROD(mark(z0), mark(z1)), MARK(z0)) MARK(prod(z0, z1)) -> c23(A__PROD(mark(z0), mark(z1)), MARK(z1)) MARK(p(z0)) -> c24(A__P(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), fact(z0)) -> c3(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) A__ADD(s(x0), if(z0, z1, z2)) -> c3(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__ADD(s(z0), z1) -> c4(A__ADD(mark(z0), mark(z1)), MARK(z1)) A__PROD(s(z0), z1) -> c7(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), MARK(z1)) A__PROD(s(z0), z1) -> c8(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z0)) A__PROD(s(z0), z1) -> c9(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z1)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(if(z0, z1, z2)) -> c20(A__IF(mark(z0), z1, z2), MARK(z0)) MARK(prod(z0, z1)) -> c22(A__PROD(mark(z0), mark(z1)), MARK(z0)) MARK(prod(z0, z1)) -> c23(A__PROD(mark(z0), mark(z1)), MARK(z1)) MARK(p(z0)) -> c24(A__P(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), fact(z0)) -> c3(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) A__ADD(s(x0), if(z0, z1, z2)) -> c3(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__PROD_2, A__IF_3, A__P_1, MARK_1, A__FACT_1 Compound Symbols: c2_1, c4_2, c7_2, c8_3, c9_3, c11_1, c12_1, c17_1, c19_2, c20_2, c22_2, c23_2, c24_2, c25_2, c26_2, c27_1, c_2, c21_1, c3_2, c3_1 ---------------------------------------- (75) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__ADD(s(z0), z1) -> c4(A__ADD(mark(z0), mark(z1)), MARK(z1)) by A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0), MARK(0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true), MARK(true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false), MARK(false)) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(true), x1) -> c4(A__ADD(true, mark(x1)), MARK(x1)) A__ADD(s(false), x1) -> c4(A__ADD(false, mark(x1)), MARK(x1)) ---------------------------------------- (76) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__PROD(s(z0), z1) -> c7(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), MARK(z1)) A__PROD(s(z0), z1) -> c8(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z0)) A__PROD(s(z0), z1) -> c9(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z1)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(if(z0, z1, z2)) -> c20(A__IF(mark(z0), z1, z2), MARK(z0)) MARK(prod(z0, z1)) -> c22(A__PROD(mark(z0), mark(z1)), MARK(z0)) MARK(prod(z0, z1)) -> c23(A__PROD(mark(z0), mark(z1)), MARK(z1)) MARK(p(z0)) -> c24(A__P(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), fact(z0)) -> c3(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) A__ADD(s(x0), if(z0, z1, z2)) -> c3(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0), MARK(0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true), MARK(true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false), MARK(false)) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(true), x1) -> c4(A__ADD(true, mark(x1)), MARK(x1)) A__ADD(s(false), x1) -> c4(A__ADD(false, mark(x1)), MARK(x1)) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__PROD(s(z0), z1) -> c7(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), MARK(z1)) A__PROD(s(z0), z1) -> c8(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z0)) A__PROD(s(z0), z1) -> c9(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z1)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(if(z0, z1, z2)) -> c20(A__IF(mark(z0), z1, z2), MARK(z0)) MARK(prod(z0, z1)) -> c22(A__PROD(mark(z0), mark(z1)), MARK(z0)) MARK(prod(z0, z1)) -> c23(A__PROD(mark(z0), mark(z1)), MARK(z1)) MARK(p(z0)) -> c24(A__P(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), fact(z0)) -> c3(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) A__ADD(s(x0), if(z0, z1, z2)) -> c3(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0), MARK(0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true), MARK(true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false), MARK(false)) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(true), x1) -> c4(A__ADD(true, mark(x1)), MARK(x1)) A__ADD(s(false), x1) -> c4(A__ADD(false, mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__PROD_2, A__IF_3, A__P_1, MARK_1, A__FACT_1 Compound Symbols: c2_1, c7_2, c8_3, c9_3, c11_1, c12_1, c17_1, c19_2, c20_2, c22_2, c23_2, c24_2, c25_2, c26_2, c27_1, c_2, c21_1, c3_2, c3_1, c4_2 ---------------------------------------- (77) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing tuple parts ---------------------------------------- (78) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__PROD(s(z0), z1) -> c7(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), MARK(z1)) A__PROD(s(z0), z1) -> c8(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z0)) A__PROD(s(z0), z1) -> c9(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z1)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(if(z0, z1, z2)) -> c20(A__IF(mark(z0), z1, z2), MARK(z0)) MARK(prod(z0, z1)) -> c22(A__PROD(mark(z0), mark(z1)), MARK(z0)) MARK(prod(z0, z1)) -> c23(A__PROD(mark(z0), mark(z1)), MARK(z1)) MARK(p(z0)) -> c24(A__P(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), fact(z0)) -> c3(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) A__ADD(s(x0), if(z0, z1, z2)) -> c3(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__PROD(s(z0), z1) -> c7(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), MARK(z1)) A__PROD(s(z0), z1) -> c8(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z0)) A__PROD(s(z0), z1) -> c9(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z1)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(if(z0, z1, z2)) -> c20(A__IF(mark(z0), z1, z2), MARK(z0)) MARK(prod(z0, z1)) -> c22(A__PROD(mark(z0), mark(z1)), MARK(z0)) MARK(prod(z0, z1)) -> c23(A__PROD(mark(z0), mark(z1)), MARK(z1)) MARK(p(z0)) -> c24(A__P(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), fact(z0)) -> c3(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) A__ADD(s(x0), if(z0, z1, z2)) -> c3(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__PROD_2, A__IF_3, A__P_1, MARK_1, A__FACT_1 Compound Symbols: c2_1, c7_2, c8_3, c9_3, c11_1, c12_1, c17_1, c19_2, c20_2, c22_2, c23_2, c24_2, c25_2, c26_2, c27_1, c_2, c21_1, c3_2, c3_1, c4_2, c4_1 ---------------------------------------- (79) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PROD(s(z0), z1) -> c7(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), MARK(z1)) by A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0)), MARK(0)) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true)), MARK(true)) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false)), MARK(false)) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0))), MARK(0)) A__PROD(s(x0), true) -> c7(A__ADD(true, a__prod(mark(x0), mark(true))), MARK(true)) A__PROD(s(x0), false) -> c7(A__ADD(false, a__prod(mark(x0), mark(false))), MARK(false)) ---------------------------------------- (80) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__PROD(s(z0), z1) -> c8(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z0)) A__PROD(s(z0), z1) -> c9(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z1)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(if(z0, z1, z2)) -> c20(A__IF(mark(z0), z1, z2), MARK(z0)) MARK(prod(z0, z1)) -> c22(A__PROD(mark(z0), mark(z1)), MARK(z0)) MARK(prod(z0, z1)) -> c23(A__PROD(mark(z0), mark(z1)), MARK(z1)) MARK(p(z0)) -> c24(A__P(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), fact(z0)) -> c3(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) A__ADD(s(x0), if(z0, z1, z2)) -> c3(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0)), MARK(0)) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true)), MARK(true)) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false)), MARK(false)) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0))), MARK(0)) A__PROD(s(x0), true) -> c7(A__ADD(true, a__prod(mark(x0), mark(true))), MARK(true)) A__PROD(s(x0), false) -> c7(A__ADD(false, a__prod(mark(x0), mark(false))), MARK(false)) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__PROD(s(z0), z1) -> c8(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z0)) A__PROD(s(z0), z1) -> c9(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z1)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(if(z0, z1, z2)) -> c20(A__IF(mark(z0), z1, z2), MARK(z0)) MARK(prod(z0, z1)) -> c22(A__PROD(mark(z0), mark(z1)), MARK(z0)) MARK(prod(z0, z1)) -> c23(A__PROD(mark(z0), mark(z1)), MARK(z1)) MARK(p(z0)) -> c24(A__P(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), fact(z0)) -> c3(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) A__ADD(s(x0), if(z0, z1, z2)) -> c3(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0)), MARK(0)) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true)), MARK(true)) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false)), MARK(false)) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0))), MARK(0)) A__PROD(s(x0), true) -> c7(A__ADD(true, a__prod(mark(x0), mark(true))), MARK(true)) A__PROD(s(x0), false) -> c7(A__ADD(false, a__prod(mark(x0), mark(false))), MARK(false)) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__PROD_2, A__IF_3, A__P_1, MARK_1, A__FACT_1 Compound Symbols: c2_1, c8_3, c9_3, c11_1, c12_1, c17_1, c19_2, c20_2, c22_2, c23_2, c24_2, c25_2, c26_2, c27_1, c_2, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2 ---------------------------------------- (81) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: A__PROD(s(x0), false) -> c7(A__ADD(false, a__prod(mark(x0), mark(false))), MARK(false)) A__PROD(s(x0), true) -> c7(A__ADD(true, a__prod(mark(x0), mark(true))), MARK(true)) ---------------------------------------- (82) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__PROD(s(z0), z1) -> c8(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z0)) A__PROD(s(z0), z1) -> c9(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z1)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(if(z0, z1, z2)) -> c20(A__IF(mark(z0), z1, z2), MARK(z0)) MARK(prod(z0, z1)) -> c22(A__PROD(mark(z0), mark(z1)), MARK(z0)) MARK(prod(z0, z1)) -> c23(A__PROD(mark(z0), mark(z1)), MARK(z1)) MARK(p(z0)) -> c24(A__P(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), fact(z0)) -> c3(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) A__ADD(s(x0), if(z0, z1, z2)) -> c3(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0)), MARK(0)) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true)), MARK(true)) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false)), MARK(false)) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0))), MARK(0)) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__PROD(s(z0), z1) -> c8(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z0)) A__PROD(s(z0), z1) -> c9(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z1)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(if(z0, z1, z2)) -> c20(A__IF(mark(z0), z1, z2), MARK(z0)) MARK(prod(z0, z1)) -> c22(A__PROD(mark(z0), mark(z1)), MARK(z0)) MARK(prod(z0, z1)) -> c23(A__PROD(mark(z0), mark(z1)), MARK(z1)) MARK(p(z0)) -> c24(A__P(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), fact(z0)) -> c3(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) A__ADD(s(x0), if(z0, z1, z2)) -> c3(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0)), MARK(0)) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true)), MARK(true)) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false)), MARK(false)) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0))), MARK(0)) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__PROD_2, A__IF_3, A__P_1, MARK_1, A__FACT_1 Compound Symbols: c2_1, c8_3, c9_3, c11_1, c12_1, c17_1, c19_2, c20_2, c22_2, c23_2, c24_2, c25_2, c26_2, c27_1, c_2, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2 ---------------------------------------- (83) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (84) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__PROD(s(z0), z1) -> c8(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z0)) A__PROD(s(z0), z1) -> c9(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z1)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(if(z0, z1, z2)) -> c20(A__IF(mark(z0), z1, z2), MARK(z0)) MARK(prod(z0, z1)) -> c22(A__PROD(mark(z0), mark(z1)), MARK(z0)) MARK(prod(z0, z1)) -> c23(A__PROD(mark(z0), mark(z1)), MARK(z1)) MARK(p(z0)) -> c24(A__P(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), fact(z0)) -> c3(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) A__ADD(s(x0), if(z0, z1, z2)) -> c3(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__PROD(s(z0), z1) -> c8(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z0)) A__PROD(s(z0), z1) -> c9(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z1)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(if(z0, z1, z2)) -> c20(A__IF(mark(z0), z1, z2), MARK(z0)) MARK(prod(z0, z1)) -> c22(A__PROD(mark(z0), mark(z1)), MARK(z0)) MARK(prod(z0, z1)) -> c23(A__PROD(mark(z0), mark(z1)), MARK(z1)) MARK(p(z0)) -> c24(A__P(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), fact(z0)) -> c3(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) A__ADD(s(x0), if(z0, z1, z2)) -> c3(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__PROD_2, A__IF_3, A__P_1, MARK_1, A__FACT_1 Compound Symbols: c2_1, c8_3, c9_3, c11_1, c12_1, c17_1, c19_2, c20_2, c22_2, c23_2, c24_2, c25_2, c26_2, c27_1, c_2, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2, c7_1 ---------------------------------------- (85) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PROD(s(z0), z1) -> c8(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z0)) by A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(0)) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(true)) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(false)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(true, a__prod(mark(x0), mark(true))), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(false, a__prod(mark(x0), mark(false))), A__PROD(mark(x0), mark(false)), MARK(x0)) ---------------------------------------- (86) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__PROD(s(z0), z1) -> c9(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z1)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(if(z0, z1, z2)) -> c20(A__IF(mark(z0), z1, z2), MARK(z0)) MARK(prod(z0, z1)) -> c22(A__PROD(mark(z0), mark(z1)), MARK(z0)) MARK(prod(z0, z1)) -> c23(A__PROD(mark(z0), mark(z1)), MARK(z1)) MARK(p(z0)) -> c24(A__P(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), fact(z0)) -> c3(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) A__ADD(s(x0), if(z0, z1, z2)) -> c3(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(0)) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(true)) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(false)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(true, a__prod(mark(x0), mark(true))), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(false, a__prod(mark(x0), mark(false))), A__PROD(mark(x0), mark(false)), MARK(x0)) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__PROD(s(z0), z1) -> c9(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z1)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(if(z0, z1, z2)) -> c20(A__IF(mark(z0), z1, z2), MARK(z0)) MARK(prod(z0, z1)) -> c22(A__PROD(mark(z0), mark(z1)), MARK(z0)) MARK(prod(z0, z1)) -> c23(A__PROD(mark(z0), mark(z1)), MARK(z1)) MARK(p(z0)) -> c24(A__P(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), fact(z0)) -> c3(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) A__ADD(s(x0), if(z0, z1, z2)) -> c3(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(0)) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(true)) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(false)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(true, a__prod(mark(x0), mark(true))), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(false, a__prod(mark(x0), mark(false))), A__PROD(mark(x0), mark(false)), MARK(x0)) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__PROD_2, A__IF_3, A__P_1, MARK_1, A__FACT_1 Compound Symbols: c2_1, c9_3, c11_1, c12_1, c17_1, c19_2, c20_2, c22_2, c23_2, c24_2, c25_2, c26_2, c27_1, c_2, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3 ---------------------------------------- (87) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing tuple parts ---------------------------------------- (88) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__PROD(s(z0), z1) -> c9(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z1)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(if(z0, z1, z2)) -> c20(A__IF(mark(z0), z1, z2), MARK(z0)) MARK(prod(z0, z1)) -> c22(A__PROD(mark(z0), mark(z1)), MARK(z0)) MARK(prod(z0, z1)) -> c23(A__PROD(mark(z0), mark(z1)), MARK(z1)) MARK(p(z0)) -> c24(A__P(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), fact(z0)) -> c3(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) A__ADD(s(x0), if(z0, z1, z2)) -> c3(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__PROD(s(z0), z1) -> c9(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z1)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(if(z0, z1, z2)) -> c20(A__IF(mark(z0), z1, z2), MARK(z0)) MARK(prod(z0, z1)) -> c22(A__PROD(mark(z0), mark(z1)), MARK(z0)) MARK(prod(z0, z1)) -> c23(A__PROD(mark(z0), mark(z1)), MARK(z1)) MARK(p(z0)) -> c24(A__P(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), fact(z0)) -> c3(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) A__ADD(s(x0), if(z0, z1, z2)) -> c3(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__PROD_2, A__IF_3, A__P_1, MARK_1, A__FACT_1 Compound Symbols: c2_1, c9_3, c11_1, c12_1, c17_1, c19_2, c20_2, c22_2, c23_2, c24_2, c25_2, c26_2, c27_1, c_2, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2 ---------------------------------------- (89) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PROD(s(z0), z1) -> c9(A__ADD(mark(z1), a__prod(mark(z0), mark(z1))), A__PROD(mark(z0), mark(z1)), MARK(z1)) by A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(0)) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(true)) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(false)) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(0)) A__PROD(s(x0), true) -> c9(A__ADD(true, a__prod(mark(x0), mark(true))), A__PROD(mark(x0), mark(true)), MARK(true)) A__PROD(s(x0), false) -> c9(A__ADD(false, a__prod(mark(x0), mark(false))), A__PROD(mark(x0), mark(false)), MARK(false)) ---------------------------------------- (90) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(if(z0, z1, z2)) -> c20(A__IF(mark(z0), z1, z2), MARK(z0)) MARK(prod(z0, z1)) -> c22(A__PROD(mark(z0), mark(z1)), MARK(z0)) MARK(prod(z0, z1)) -> c23(A__PROD(mark(z0), mark(z1)), MARK(z1)) MARK(p(z0)) -> c24(A__P(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), fact(z0)) -> c3(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) A__ADD(s(x0), if(z0, z1, z2)) -> c3(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(0)) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(true)) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(false)) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(0)) A__PROD(s(x0), true) -> c9(A__ADD(true, a__prod(mark(x0), mark(true))), A__PROD(mark(x0), mark(true)), MARK(true)) A__PROD(s(x0), false) -> c9(A__ADD(false, a__prod(mark(x0), mark(false))), A__PROD(mark(x0), mark(false)), MARK(false)) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(if(z0, z1, z2)) -> c20(A__IF(mark(z0), z1, z2), MARK(z0)) MARK(prod(z0, z1)) -> c22(A__PROD(mark(z0), mark(z1)), MARK(z0)) MARK(prod(z0, z1)) -> c23(A__PROD(mark(z0), mark(z1)), MARK(z1)) MARK(p(z0)) -> c24(A__P(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), fact(z0)) -> c3(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) A__ADD(s(x0), if(z0, z1, z2)) -> c3(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(0)) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(true)) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(false)) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(0)) A__PROD(s(x0), true) -> c9(A__ADD(true, a__prod(mark(x0), mark(true))), A__PROD(mark(x0), mark(true)), MARK(true)) A__PROD(s(x0), false) -> c9(A__ADD(false, a__prod(mark(x0), mark(false))), A__PROD(mark(x0), mark(false)), MARK(false)) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__FACT_1, A__PROD_2 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c20_2, c22_2, c23_2, c24_2, c25_2, c26_2, c27_1, c_2, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3 ---------------------------------------- (91) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 8 trailing tuple parts ---------------------------------------- (92) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(if(z0, z1, z2)) -> c20(A__IF(mark(z0), z1, z2), MARK(z0)) MARK(prod(z0, z1)) -> c22(A__PROD(mark(z0), mark(z1)), MARK(z0)) MARK(prod(z0, z1)) -> c23(A__PROD(mark(z0), mark(z1)), MARK(z1)) MARK(p(z0)) -> c24(A__P(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), fact(z0)) -> c3(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) A__ADD(s(x0), if(z0, z1, z2)) -> c3(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(if(z0, z1, z2)) -> c20(A__IF(mark(z0), z1, z2), MARK(z0)) MARK(prod(z0, z1)) -> c22(A__PROD(mark(z0), mark(z1)), MARK(z0)) MARK(prod(z0, z1)) -> c23(A__PROD(mark(z0), mark(z1)), MARK(z1)) MARK(p(z0)) -> c24(A__P(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), fact(z0)) -> c3(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) A__ADD(s(x0), if(z0, z1, z2)) -> c3(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__FACT_1, A__PROD_2 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c20_2, c22_2, c23_2, c24_2, c25_2, c26_2, c27_1, c_2, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1 ---------------------------------------- (93) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(if(z0, z1, z2)) -> c20(A__IF(mark(z0), z1, z2), MARK(z0)) by MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(A__IF(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(if(0, x1, x2)) -> c20(A__IF(0, x1, x2), MARK(0)) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2), MARK(true)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2), MARK(false)) ---------------------------------------- (94) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(prod(z0, z1)) -> c22(A__PROD(mark(z0), mark(z1)), MARK(z0)) MARK(prod(z0, z1)) -> c23(A__PROD(mark(z0), mark(z1)), MARK(z1)) MARK(p(z0)) -> c24(A__P(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), fact(z0)) -> c3(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) A__ADD(s(x0), if(z0, z1, z2)) -> c3(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(A__IF(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(if(0, x1, x2)) -> c20(A__IF(0, x1, x2), MARK(0)) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2), MARK(true)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2), MARK(false)) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(prod(z0, z1)) -> c22(A__PROD(mark(z0), mark(z1)), MARK(z0)) MARK(prod(z0, z1)) -> c23(A__PROD(mark(z0), mark(z1)), MARK(z1)) MARK(p(z0)) -> c24(A__P(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), fact(z0)) -> c3(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) A__ADD(s(x0), if(z0, z1, z2)) -> c3(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(A__IF(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(if(0, x1, x2)) -> c20(A__IF(0, x1, x2), MARK(0)) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2), MARK(true)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2), MARK(false)) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__FACT_1, A__PROD_2 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c22_2, c23_2, c24_2, c25_2, c26_2, c27_1, c_2, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2 ---------------------------------------- (95) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(if(0, x1, x2)) -> c20(A__IF(0, x1, x2), MARK(0)) ---------------------------------------- (96) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(prod(z0, z1)) -> c22(A__PROD(mark(z0), mark(z1)), MARK(z0)) MARK(prod(z0, z1)) -> c23(A__PROD(mark(z0), mark(z1)), MARK(z1)) MARK(p(z0)) -> c24(A__P(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), fact(z0)) -> c3(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) A__ADD(s(x0), if(z0, z1, z2)) -> c3(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(A__IF(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2), MARK(true)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2), MARK(false)) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(prod(z0, z1)) -> c22(A__PROD(mark(z0), mark(z1)), MARK(z0)) MARK(prod(z0, z1)) -> c23(A__PROD(mark(z0), mark(z1)), MARK(z1)) MARK(p(z0)) -> c24(A__P(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), fact(z0)) -> c3(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) A__ADD(s(x0), if(z0, z1, z2)) -> c3(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(A__IF(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2), MARK(true)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2), MARK(false)) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__FACT_1, A__PROD_2 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c22_2, c23_2, c24_2, c25_2, c26_2, c27_1, c_2, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2 ---------------------------------------- (97) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (98) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(prod(z0, z1)) -> c22(A__PROD(mark(z0), mark(z1)), MARK(z0)) MARK(prod(z0, z1)) -> c23(A__PROD(mark(z0), mark(z1)), MARK(z1)) MARK(p(z0)) -> c24(A__P(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), fact(z0)) -> c3(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) A__ADD(s(x0), if(z0, z1, z2)) -> c3(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(prod(z0, z1)) -> c22(A__PROD(mark(z0), mark(z1)), MARK(z0)) MARK(prod(z0, z1)) -> c23(A__PROD(mark(z0), mark(z1)), MARK(z1)) MARK(p(z0)) -> c24(A__P(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), fact(z0)) -> c3(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) A__ADD(s(x0), if(z0, z1, z2)) -> c3(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__FACT_1, A__PROD_2 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c22_2, c23_2, c24_2, c25_2, c26_2, c27_1, c_2, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1 ---------------------------------------- (99) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(prod(z0, z1)) -> c22(A__PROD(mark(z0), mark(z1)), MARK(z0)) by MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(0, x1)) -> c22(A__PROD(0, mark(x1)), MARK(0)) MARK(prod(true, x1)) -> c22(A__PROD(true, mark(x1)), MARK(true)) MARK(prod(false, x1)) -> c22(A__PROD(false, mark(x1)), MARK(false)) ---------------------------------------- (100) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(prod(z0, z1)) -> c23(A__PROD(mark(z0), mark(z1)), MARK(z1)) MARK(p(z0)) -> c24(A__P(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), fact(z0)) -> c3(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) A__ADD(s(x0), if(z0, z1, z2)) -> c3(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(0, x1)) -> c22(A__PROD(0, mark(x1)), MARK(0)) MARK(prod(true, x1)) -> c22(A__PROD(true, mark(x1)), MARK(true)) MARK(prod(false, x1)) -> c22(A__PROD(false, mark(x1)), MARK(false)) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(prod(z0, z1)) -> c23(A__PROD(mark(z0), mark(z1)), MARK(z1)) MARK(p(z0)) -> c24(A__P(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), fact(z0)) -> c3(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) A__ADD(s(x0), if(z0, z1, z2)) -> c3(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(0, x1)) -> c22(A__PROD(0, mark(x1)), MARK(0)) MARK(prod(true, x1)) -> c22(A__PROD(true, mark(x1)), MARK(true)) MARK(prod(false, x1)) -> c22(A__PROD(false, mark(x1)), MARK(false)) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__FACT_1, A__PROD_2 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c23_2, c24_2, c25_2, c26_2, c27_1, c_2, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2 ---------------------------------------- (101) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing nodes: MARK(prod(true, x1)) -> c22(A__PROD(true, mark(x1)), MARK(true)) MARK(prod(false, x1)) -> c22(A__PROD(false, mark(x1)), MARK(false)) MARK(prod(0, x1)) -> c22(A__PROD(0, mark(x1)), MARK(0)) ---------------------------------------- (102) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(prod(z0, z1)) -> c23(A__PROD(mark(z0), mark(z1)), MARK(z1)) MARK(p(z0)) -> c24(A__P(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), fact(z0)) -> c3(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) A__ADD(s(x0), if(z0, z1, z2)) -> c3(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(prod(z0, z1)) -> c23(A__PROD(mark(z0), mark(z1)), MARK(z1)) MARK(p(z0)) -> c24(A__P(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), fact(z0)) -> c3(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) A__ADD(s(x0), if(z0, z1, z2)) -> c3(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__FACT_1, A__PROD_2 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c23_2, c24_2, c25_2, c26_2, c27_1, c_2, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2 ---------------------------------------- (103) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(prod(z0, z1)) -> c23(A__PROD(mark(z0), mark(z1)), MARK(z1)) by MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0), MARK(0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true), MARK(true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false), MARK(false)) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(0, x1)) -> c23(A__PROD(0, mark(x1)), MARK(x1)) MARK(prod(true, x1)) -> c23(A__PROD(true, mark(x1)), MARK(x1)) MARK(prod(false, x1)) -> c23(A__PROD(false, mark(x1)), MARK(x1)) ---------------------------------------- (104) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(p(z0)) -> c24(A__P(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), fact(z0)) -> c3(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) A__ADD(s(x0), if(z0, z1, z2)) -> c3(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0), MARK(0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true), MARK(true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false), MARK(false)) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(0, x1)) -> c23(A__PROD(0, mark(x1)), MARK(x1)) MARK(prod(true, x1)) -> c23(A__PROD(true, mark(x1)), MARK(x1)) MARK(prod(false, x1)) -> c23(A__PROD(false, mark(x1)), MARK(x1)) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(p(z0)) -> c24(A__P(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), fact(z0)) -> c3(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) A__ADD(s(x0), if(z0, z1, z2)) -> c3(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0), MARK(0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true), MARK(true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false), MARK(false)) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(0, x1)) -> c23(A__PROD(0, mark(x1)), MARK(x1)) MARK(prod(true, x1)) -> c23(A__PROD(true, mark(x1)), MARK(x1)) MARK(prod(false, x1)) -> c23(A__PROD(false, mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__FACT_1, A__PROD_2 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c24_2, c25_2, c26_2, c27_1, c_2, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2 ---------------------------------------- (105) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 6 trailing tuple parts ---------------------------------------- (106) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(p(z0)) -> c24(A__P(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), fact(z0)) -> c3(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) A__ADD(s(x0), if(z0, z1, z2)) -> c3(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(p(z0)) -> c24(A__P(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), fact(z0)) -> c3(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) A__ADD(s(x0), if(z0, z1, z2)) -> c3(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__FACT_1, A__PROD_2 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c24_2, c25_2, c26_2, c27_1, c_2, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1 ---------------------------------------- (107) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(p(z0)) -> c24(A__P(mark(z0)), MARK(z0)) by MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(p(0)) -> c24(A__P(0), MARK(0)) MARK(p(true)) -> c24(A__P(true), MARK(true)) MARK(p(false)) -> c24(A__P(false), MARK(false)) ---------------------------------------- (108) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), fact(z0)) -> c3(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) A__ADD(s(x0), if(z0, z1, z2)) -> c3(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(p(0)) -> c24(A__P(0), MARK(0)) MARK(p(true)) -> c24(A__P(true), MARK(true)) MARK(p(false)) -> c24(A__P(false), MARK(false)) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), fact(z0)) -> c3(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) A__ADD(s(x0), if(z0, z1, z2)) -> c3(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(p(0)) -> c24(A__P(0), MARK(0)) MARK(p(true)) -> c24(A__P(true), MARK(true)) MARK(p(false)) -> c24(A__P(false), MARK(false)) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__FACT_1, A__PROD_2 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c25_2, c26_2, c27_1, c_2, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1, c24_2 ---------------------------------------- (109) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing nodes: MARK(p(false)) -> c24(A__P(false), MARK(false)) MARK(p(0)) -> c24(A__P(0), MARK(0)) MARK(p(true)) -> c24(A__P(true), MARK(true)) ---------------------------------------- (110) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), fact(z0)) -> c3(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) A__ADD(s(x0), if(z0, z1, z2)) -> c3(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), fact(z0)) -> c3(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) A__ADD(s(x0), if(z0, z1, z2)) -> c3(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__FACT_1, A__PROD_2 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c25_2, c26_2, c27_1, c_2, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1, c24_2 ---------------------------------------- (111) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(add(z0, z1)) -> c25(A__ADD(mark(z0), mark(z1)), MARK(z0)) by MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1)), MARK(0)) MARK(add(true, x1)) -> c25(A__ADD(true, mark(x1)), MARK(true)) MARK(add(false, x1)) -> c25(A__ADD(false, mark(x1)), MARK(false)) ---------------------------------------- (112) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), fact(z0)) -> c3(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) A__ADD(s(x0), if(z0, z1, z2)) -> c3(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1)), MARK(0)) MARK(add(true, x1)) -> c25(A__ADD(true, mark(x1)), MARK(true)) MARK(add(false, x1)) -> c25(A__ADD(false, mark(x1)), MARK(false)) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), fact(z0)) -> c3(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) A__ADD(s(x0), if(z0, z1, z2)) -> c3(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1)), MARK(0)) MARK(add(true, x1)) -> c25(A__ADD(true, mark(x1)), MARK(true)) MARK(add(false, x1)) -> c25(A__ADD(false, mark(x1)), MARK(false)) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__FACT_1, A__PROD_2 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c26_2, c27_1, c_2, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1, c24_2, c25_2 ---------------------------------------- (113) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(add(false, x1)) -> c25(A__ADD(false, mark(x1)), MARK(false)) MARK(add(true, x1)) -> c25(A__ADD(true, mark(x1)), MARK(true)) ---------------------------------------- (114) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), fact(z0)) -> c3(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) A__ADD(s(x0), if(z0, z1, z2)) -> c3(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1)), MARK(0)) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), fact(z0)) -> c3(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) A__ADD(s(x0), if(z0, z1, z2)) -> c3(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1)), MARK(0)) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__FACT_1, A__PROD_2 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c26_2, c27_1, c_2, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1, c24_2, c25_2 ---------------------------------------- (115) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (116) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), fact(z0)) -> c3(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) A__ADD(s(x0), if(z0, z1, z2)) -> c3(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c27(MARK(z0)) A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), fact(z0)) -> c3(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) A__ADD(s(x0), if(z0, z1, z2)) -> c3(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__FACT_1, A__PROD_2 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c26_2, c27_1, c_2, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1, c24_2, c25_2, c25_1 ---------------------------------------- (117) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(add(z0, z1)) -> c26(A__ADD(mark(z0), mark(z1)), MARK(z1)) by MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0), MARK(0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true), MARK(true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false), MARK(false)) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(true, x1)) -> c26(A__ADD(true, mark(x1)), MARK(x1)) MARK(add(false, x1)) -> c26(A__ADD(false, mark(x1)), MARK(x1)) ---------------------------------------- (118) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), fact(z0)) -> c3(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) A__ADD(s(x0), if(z0, z1, z2)) -> c3(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0), MARK(0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true), MARK(true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false), MARK(false)) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(true, x1)) -> c26(A__ADD(true, mark(x1)), MARK(x1)) MARK(add(false, x1)) -> c26(A__ADD(false, mark(x1)), MARK(x1)) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), fact(z0)) -> c3(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) A__ADD(s(x0), if(z0, z1, z2)) -> c3(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0), MARK(0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true), MARK(true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false), MARK(false)) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(true, x1)) -> c26(A__ADD(true, mark(x1)), MARK(x1)) MARK(add(false, x1)) -> c26(A__ADD(false, mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__FACT_1, A__PROD_2 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c27_1, c_2, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1, c24_2, c25_2, c25_1, c26_2 ---------------------------------------- (119) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing tuple parts ---------------------------------------- (120) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), fact(z0)) -> c3(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) A__ADD(s(x0), if(z0, z1, z2)) -> c3(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), fact(z0)) -> c3(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) A__ADD(s(x0), if(z0, z1, z2)) -> c3(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__FACT_1, A__PROD_2 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c27_1, c_2, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1, c24_2, c25_2, c25_1, c26_2, c26_1 ---------------------------------------- (121) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__FACT(z0) -> c(A__IF(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))), MARK(z0)) by A__FACT(x0) -> c(A__IF(zero(mark(x0)), s(0), prod(x0, fact(p(x0)))), MARK(x0)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0)))), MARK(0)) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true)))), MARK(true)) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false)))), MARK(false)) ---------------------------------------- (122) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), fact(z0)) -> c3(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) A__ADD(s(x0), if(z0, z1, z2)) -> c3(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(x0) -> c(A__IF(zero(mark(x0)), s(0), prod(x0, fact(p(x0)))), MARK(x0)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0)))), MARK(0)) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true)))), MARK(true)) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false)))), MARK(false)) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), fact(z0)) -> c3(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) A__ADD(s(x0), if(z0, z1, z2)) -> c3(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(x0) -> c(A__IF(zero(mark(x0)), s(0), prod(x0, fact(p(x0)))), MARK(x0)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0)))), MARK(0)) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true)))), MARK(true)) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false)))), MARK(false)) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__PROD_2, A__FACT_1 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c27_1, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1, c24_2, c25_2, c25_1, c26_2, c26_1, c_2 ---------------------------------------- (123) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (124) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), fact(z0)) -> c3(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) A__ADD(s(x0), if(z0, z1, z2)) -> c3(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), fact(z0)) -> c3(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) A__ADD(s(x0), if(z0, z1, z2)) -> c3(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__PROD_2, A__FACT_1 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c27_1, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1, c24_2, c25_2, c25_1, c26_2, c26_1, c_2, c_1 ---------------------------------------- (125) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__ADD(s(x0), fact(z0)) -> c3(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) by A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1))), MARK(0)) A__ADD(s(true), fact(x1)) -> c3(A__ADD(true, a__fact(mark(x1))), MARK(true)) A__ADD(s(false), fact(x1)) -> c3(A__ADD(false, a__fact(mark(x1))), MARK(false)) ---------------------------------------- (126) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), if(z0, z1, z2)) -> c3(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1))), MARK(0)) A__ADD(s(true), fact(x1)) -> c3(A__ADD(true, a__fact(mark(x1))), MARK(true)) A__ADD(s(false), fact(x1)) -> c3(A__ADD(false, a__fact(mark(x1))), MARK(false)) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), if(z0, z1, z2)) -> c3(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1))), MARK(0)) A__ADD(s(true), fact(x1)) -> c3(A__ADD(true, a__fact(mark(x1))), MARK(true)) A__ADD(s(false), fact(x1)) -> c3(A__ADD(false, a__fact(mark(x1))), MARK(false)) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__PROD_2, A__FACT_1 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c27_1, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1, c24_2, c25_2, c25_1, c26_2, c26_1, c_2, c_1 ---------------------------------------- (127) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: A__ADD(s(false), fact(x1)) -> c3(A__ADD(false, a__fact(mark(x1))), MARK(false)) A__ADD(s(true), fact(x1)) -> c3(A__ADD(true, a__fact(mark(x1))), MARK(true)) ---------------------------------------- (128) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), if(z0, z1, z2)) -> c3(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) 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a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1))), MARK(0)) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), if(z0, z1, z2)) -> c3(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1))), MARK(0)) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__PROD_2, A__FACT_1 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c27_1, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1, c24_2, c25_2, c25_1, c26_2, c26_1, c_2, c_1 ---------------------------------------- (129) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (130) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), if(z0, z1, z2)) -> c3(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), if(z0, z1, z2)) -> c3(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__PROD_2, A__FACT_1 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c27_1, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1, c24_2, c25_2, c25_1, c26_2, c26_1, c_2, c_1 ---------------------------------------- (131) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__ADD(s(x0), if(z0, z1, z2)) -> c3(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) by A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3)), MARK(0)) A__ADD(s(true), if(x1, x2, x3)) -> c3(A__ADD(true, a__if(mark(x1), x2, x3)), MARK(true)) A__ADD(s(false), if(x1, x2, x3)) -> c3(A__ADD(false, a__if(mark(x1), x2, x3)), MARK(false)) ---------------------------------------- (132) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), 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fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3)), MARK(0)) A__ADD(s(true), if(x1, x2, x3)) -> c3(A__ADD(true, a__if(mark(x1), x2, x3)), MARK(true)) A__ADD(s(false), if(x1, x2, x3)) -> c3(A__ADD(false, a__if(mark(x1), x2, x3)), MARK(false)) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3)), MARK(0)) A__ADD(s(true), if(x1, x2, x3)) -> c3(A__ADD(true, a__if(mark(x1), x2, x3)), MARK(true)) A__ADD(s(false), if(x1, x2, x3)) -> c3(A__ADD(false, a__if(mark(x1), x2, x3)), MARK(false)) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__PROD_2, A__FACT_1 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c27_1, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1, c24_2, c25_2, c25_1, c26_2, c26_1, c_2, c_1 ---------------------------------------- (133) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: A__ADD(s(false), if(x1, x2, x3)) -> c3(A__ADD(false, a__if(mark(x1), x2, x3)), MARK(false)) A__ADD(s(true), if(x1, x2, x3)) -> c3(A__ADD(true, a__if(mark(x1), x2, x3)), MARK(true)) ---------------------------------------- (134) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3)), MARK(0)) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3)), MARK(0)) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__PROD_2, A__FACT_1 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c27_1, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1, c24_2, c25_2, c25_1, c26_2, c26_1, c_2, c_1 ---------------------------------------- (135) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (136) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__PROD_2, A__FACT_1 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c27_1, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1, c24_2, c25_2, c25_1, c26_2, c26_1, c_2, c_1 ---------------------------------------- (137) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__ADD(s(x0), zero(z0)) -> c3(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) by A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1))), MARK(0)) A__ADD(s(true), zero(x1)) -> c3(A__ADD(true, a__zero(mark(x1))), MARK(true)) A__ADD(s(false), zero(x1)) -> c3(A__ADD(false, a__zero(mark(x1))), MARK(false)) ---------------------------------------- (138) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1))), MARK(0)) A__ADD(s(true), zero(x1)) -> c3(A__ADD(true, a__zero(mark(x1))), MARK(true)) A__ADD(s(false), zero(x1)) -> c3(A__ADD(false, a__zero(mark(x1))), MARK(false)) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1))), MARK(0)) A__ADD(s(true), zero(x1)) -> c3(A__ADD(true, a__zero(mark(x1))), MARK(true)) A__ADD(s(false), zero(x1)) -> c3(A__ADD(false, a__zero(mark(x1))), MARK(false)) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__PROD_2, A__FACT_1 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c27_1, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1, c24_2, c25_2, c25_1, c26_2, c26_1, c_2, c_1 ---------------------------------------- (139) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: A__ADD(s(true), zero(x1)) -> c3(A__ADD(true, a__zero(mark(x1))), MARK(true)) A__ADD(s(false), zero(x1)) -> c3(A__ADD(false, a__zero(mark(x1))), MARK(false)) ---------------------------------------- (140) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1))), MARK(0)) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1))), MARK(0)) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__PROD_2, A__FACT_1 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c27_1, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1, c24_2, c25_2, c25_1, c26_2, c26_1, c_2, c_1 ---------------------------------------- (141) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (142) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1)))) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1)))) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__PROD_2, A__FACT_1 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c27_1, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1, c24_2, c25_2, c25_1, c26_2, c26_1, c_2, c_1 ---------------------------------------- (143) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__ADD(s(x0), prod(z0, z1)) -> c3(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) by A__ADD(s(x0), prod(x1, x2)) -> c3(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), prod(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, p(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, s(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, 0)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), prod(x1, true)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(x0)) A__ADD(s(x0), prod(x1, false)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(x0)) A__ADD(s(x0), prod(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(p(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(0, x2)) -> c3(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(true, x2)) -> c3(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(false, x2)) -> c3(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), prod(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2))), MARK(0)) A__ADD(s(true), prod(x1, x2)) -> c3(A__ADD(true, a__prod(mark(x1), mark(x2))), MARK(true)) A__ADD(s(false), prod(x1, x2)) -> c3(A__ADD(false, a__prod(mark(x1), mark(x2))), MARK(false)) ---------------------------------------- (144) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, 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a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1)))) A__ADD(s(x0), prod(x1, x2)) -> c3(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), prod(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, p(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, s(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, 0)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), prod(x1, true)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(x0)) A__ADD(s(x0), prod(x1, false)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(x0)) A__ADD(s(x0), prod(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(p(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(0, x2)) -> c3(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(true, x2)) -> c3(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(false, x2)) -> c3(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), prod(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2))), MARK(0)) A__ADD(s(true), prod(x1, x2)) -> c3(A__ADD(true, a__prod(mark(x1), mark(x2))), MARK(true)) A__ADD(s(false), prod(x1, x2)) -> c3(A__ADD(false, a__prod(mark(x1), mark(x2))), MARK(false)) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1)))) A__ADD(s(x0), prod(x1, x2)) -> c3(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), prod(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, p(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, s(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, 0)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), prod(x1, true)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(x0)) A__ADD(s(x0), prod(x1, false)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(x0)) A__ADD(s(x0), prod(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(p(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(0, x2)) -> c3(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(true, x2)) -> c3(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(false, x2)) -> c3(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), prod(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2))), MARK(0)) A__ADD(s(true), prod(x1, x2)) -> c3(A__ADD(true, a__prod(mark(x1), mark(x2))), MARK(true)) A__ADD(s(false), prod(x1, x2)) -> c3(A__ADD(false, a__prod(mark(x1), mark(x2))), MARK(false)) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__PROD_2, A__FACT_1 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c27_1, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1, c24_2, c25_2, c25_1, c26_2, c26_1, c_2, c_1 ---------------------------------------- (145) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: A__ADD(s(true), prod(x1, x2)) -> c3(A__ADD(true, a__prod(mark(x1), mark(x2))), MARK(true)) A__ADD(s(false), prod(x1, x2)) -> c3(A__ADD(false, a__prod(mark(x1), mark(x2))), MARK(false)) ---------------------------------------- (146) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1)))) A__ADD(s(x0), prod(x1, x2)) -> c3(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), prod(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, p(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, s(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, 0)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), prod(x1, true)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(x0)) A__ADD(s(x0), prod(x1, false)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(x0)) A__ADD(s(x0), prod(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(p(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(0, x2)) -> c3(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(true, x2)) -> c3(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(false, x2)) -> c3(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), prod(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2))), MARK(0)) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1)))) A__ADD(s(x0), prod(x1, x2)) -> c3(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), prod(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, p(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, s(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, 0)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), prod(x1, true)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(x0)) A__ADD(s(x0), prod(x1, false)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(x0)) A__ADD(s(x0), prod(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(p(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(0, x2)) -> c3(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(true, x2)) -> c3(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(false, x2)) -> c3(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), prod(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2))), MARK(0)) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__PROD_2, A__FACT_1 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c27_1, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1, c24_2, c25_2, c25_1, c26_2, c26_1, c_2, c_1 ---------------------------------------- (147) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (148) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), 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MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), 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x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1)))) A__ADD(s(x0), prod(x1, x2)) -> c3(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), prod(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, p(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, s(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, 0)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), prod(x1, true)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(x0)) A__ADD(s(x0), prod(x1, false)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(x0)) A__ADD(s(x0), prod(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(p(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(0, x2)) -> c3(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(true, x2)) -> c3(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(false, x2)) -> c3(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), prod(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2)))) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1)))) A__ADD(s(x0), prod(x1, x2)) -> c3(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), prod(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, p(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, s(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, 0)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), prod(x1, true)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(x0)) A__ADD(s(x0), prod(x1, false)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(x0)) A__ADD(s(x0), prod(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(p(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(0, x2)) -> c3(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(true, x2)) -> c3(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(false, x2)) -> c3(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), prod(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2)))) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__PROD_2, A__FACT_1 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c27_1, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1, c24_2, c25_2, c25_1, c26_2, c26_1, c_2, c_1 ---------------------------------------- (149) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__ADD(s(x0), p(z0)) -> c3(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) by A__ADD(s(x0), p(x1)) -> c3(A__ADD(mark(x0), p(mark(x1))), MARK(x0)) A__ADD(s(x0), p(fact(z0))) -> c3(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), p(zero(z0))) -> c3(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(p(z0))) -> c3(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(add(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(s(z0))) -> c3(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(0)) -> c3(A__ADD(mark(x0), a__p(0)), MARK(x0)) A__ADD(s(x0), p(true)) -> c3(A__ADD(mark(x0), a__p(true)), MARK(x0)) A__ADD(s(x0), p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1))), MARK(0)) A__ADD(s(true), p(x1)) -> c3(A__ADD(true, a__p(mark(x1))), MARK(true)) A__ADD(s(false), p(x1)) -> c3(A__ADD(false, a__p(mark(x1))), MARK(false)) ---------------------------------------- (150) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1)))) A__ADD(s(x0), prod(x1, x2)) -> c3(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), prod(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, p(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, s(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, 0)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), prod(x1, true)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(x0)) A__ADD(s(x0), prod(x1, false)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(x0)) A__ADD(s(x0), prod(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(p(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(0, x2)) -> c3(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(true, x2)) -> c3(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(false, x2)) -> c3(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), prod(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2)))) A__ADD(s(x0), p(x1)) -> c3(A__ADD(mark(x0), p(mark(x1))), MARK(x0)) A__ADD(s(x0), p(fact(z0))) -> c3(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), p(zero(z0))) -> c3(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(p(z0))) -> c3(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(add(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(s(z0))) -> c3(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(0)) -> c3(A__ADD(mark(x0), a__p(0)), MARK(x0)) A__ADD(s(x0), p(true)) -> c3(A__ADD(mark(x0), a__p(true)), MARK(x0)) A__ADD(s(x0), p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1))), MARK(0)) A__ADD(s(true), p(x1)) -> c3(A__ADD(true, a__p(mark(x1))), MARK(true)) A__ADD(s(false), p(x1)) -> c3(A__ADD(false, a__p(mark(x1))), MARK(false)) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1)))) A__ADD(s(x0), prod(x1, x2)) -> c3(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), prod(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, p(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, s(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, 0)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), prod(x1, true)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(x0)) A__ADD(s(x0), prod(x1, false)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(x0)) A__ADD(s(x0), prod(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(p(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(0, x2)) -> c3(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(true, x2)) -> c3(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(false, x2)) -> c3(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), prod(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2)))) A__ADD(s(x0), p(x1)) -> c3(A__ADD(mark(x0), p(mark(x1))), MARK(x0)) A__ADD(s(x0), p(fact(z0))) -> c3(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), p(zero(z0))) -> c3(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(p(z0))) -> c3(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(add(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(s(z0))) -> c3(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(0)) -> c3(A__ADD(mark(x0), a__p(0)), MARK(x0)) A__ADD(s(x0), p(true)) -> c3(A__ADD(mark(x0), a__p(true)), MARK(x0)) A__ADD(s(x0), p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1))), MARK(0)) A__ADD(s(true), p(x1)) -> c3(A__ADD(true, a__p(mark(x1))), MARK(true)) A__ADD(s(false), p(x1)) -> c3(A__ADD(false, a__p(mark(x1))), MARK(false)) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__PROD_2, A__FACT_1 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c27_1, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1, c24_2, c25_2, c25_1, c26_2, c26_1, c_2, c_1 ---------------------------------------- (151) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: A__ADD(s(true), p(x1)) -> c3(A__ADD(true, a__p(mark(x1))), MARK(true)) A__ADD(s(false), p(x1)) -> c3(A__ADD(false, a__p(mark(x1))), MARK(false)) ---------------------------------------- (152) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1)))) A__ADD(s(x0), prod(x1, x2)) -> c3(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), prod(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, p(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, s(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, 0)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), prod(x1, true)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(x0)) A__ADD(s(x0), prod(x1, false)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(x0)) A__ADD(s(x0), prod(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(p(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(0, x2)) -> c3(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(true, x2)) -> c3(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(false, x2)) -> c3(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), prod(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2)))) A__ADD(s(x0), p(x1)) -> c3(A__ADD(mark(x0), p(mark(x1))), MARK(x0)) A__ADD(s(x0), p(fact(z0))) -> c3(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), p(zero(z0))) -> c3(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(p(z0))) -> c3(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(add(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(s(z0))) -> c3(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(0)) -> c3(A__ADD(mark(x0), a__p(0)), MARK(x0)) A__ADD(s(x0), p(true)) -> c3(A__ADD(mark(x0), a__p(true)), MARK(x0)) A__ADD(s(x0), p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1))), MARK(0)) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) 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MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) 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c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), 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c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1)))) A__ADD(s(x0), prod(x1, x2)) -> c3(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), prod(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, p(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, s(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, 0)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), prod(x1, true)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(x0)) A__ADD(s(x0), prod(x1, false)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(x0)) A__ADD(s(x0), prod(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(p(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(0, x2)) -> c3(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(true, x2)) -> c3(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(false, x2)) -> c3(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), prod(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2)))) A__ADD(s(x0), p(x1)) -> c3(A__ADD(mark(x0), p(mark(x1))), MARK(x0)) A__ADD(s(x0), p(fact(z0))) -> c3(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), p(zero(z0))) -> c3(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(p(z0))) -> c3(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(add(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(s(z0))) -> c3(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(0)) -> c3(A__ADD(mark(x0), a__p(0)), MARK(x0)) A__ADD(s(x0), p(true)) -> c3(A__ADD(mark(x0), a__p(true)), MARK(x0)) A__ADD(s(x0), p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1))), MARK(0)) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__PROD_2, A__FACT_1 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c27_1, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1, c24_2, c25_2, c25_1, c26_2, c26_1, c_2, c_1 ---------------------------------------- (153) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (154) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1)))) A__ADD(s(x0), prod(x1, x2)) -> c3(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), prod(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, p(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, s(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, 0)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), prod(x1, true)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(x0)) A__ADD(s(x0), prod(x1, false)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(x0)) A__ADD(s(x0), prod(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(p(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(0, x2)) -> c3(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(true, x2)) -> c3(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(false, x2)) -> c3(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), prod(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2)))) A__ADD(s(x0), p(x1)) -> c3(A__ADD(mark(x0), p(mark(x1))), MARK(x0)) A__ADD(s(x0), p(fact(z0))) -> c3(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), p(zero(z0))) -> c3(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(p(z0))) -> c3(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(add(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(s(z0))) -> c3(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(0)) -> c3(A__ADD(mark(x0), a__p(0)), MARK(x0)) A__ADD(s(x0), p(true)) -> c3(A__ADD(mark(x0), a__p(true)), MARK(x0)) A__ADD(s(x0), p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1)))) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> 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c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1)))) A__ADD(s(x0), prod(x1, x2)) -> c3(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), prod(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, p(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, s(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, 0)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), prod(x1, true)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(x0)) A__ADD(s(x0), prod(x1, false)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(x0)) A__ADD(s(x0), prod(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(p(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(0, x2)) -> c3(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(true, x2)) -> c3(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(false, x2)) -> c3(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), prod(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2)))) A__ADD(s(x0), p(x1)) -> c3(A__ADD(mark(x0), p(mark(x1))), MARK(x0)) A__ADD(s(x0), p(fact(z0))) -> c3(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), p(zero(z0))) -> c3(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(p(z0))) -> c3(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(add(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(s(z0))) -> c3(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(0)) -> c3(A__ADD(mark(x0), a__p(0)), MARK(x0)) A__ADD(s(x0), p(true)) -> c3(A__ADD(mark(x0), a__p(true)), MARK(x0)) A__ADD(s(x0), p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1)))) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__PROD_2, A__FACT_1 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c27_1, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1, c24_2, c25_2, c25_1, c26_2, c26_1, c_2, c_1 ---------------------------------------- (155) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__ADD(s(x0), add(z0, z1)) -> c3(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) by A__ADD(s(x0), add(x1, x2)) -> c3(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), add(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), add(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, p(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, s(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, 0)) -> c3(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), add(x1, true)) -> c3(A__ADD(mark(x0), a__add(mark(x1), true)), MARK(x0)) A__ADD(s(x0), add(x1, false)) -> c3(A__ADD(mark(x0), a__add(mark(x1), false)), MARK(x0)) A__ADD(s(x0), add(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), add(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(p(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(s(z0), x2)) -> c3(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(0, x2)) -> c3(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) A__ADD(s(x0), add(true, x2)) -> c3(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(x0)) A__ADD(s(x0), add(false, x2)) -> c3(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), add(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), add(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), add(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__add(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), add(x1, x2)) -> c3(A__ADD(0, a__add(mark(x1), mark(x2))), MARK(0)) A__ADD(s(true), add(x1, x2)) -> c3(A__ADD(true, a__add(mark(x1), mark(x2))), MARK(true)) A__ADD(s(false), add(x1, x2)) -> c3(A__ADD(false, a__add(mark(x1), mark(x2))), MARK(false)) ---------------------------------------- (156) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1)))) A__ADD(s(x0), prod(x1, x2)) -> c3(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), prod(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, p(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, s(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, 0)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), prod(x1, true)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(x0)) A__ADD(s(x0), prod(x1, false)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(x0)) A__ADD(s(x0), prod(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(p(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(0, x2)) -> c3(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(true, x2)) -> c3(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(false, x2)) -> c3(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), prod(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2)))) A__ADD(s(x0), p(x1)) -> c3(A__ADD(mark(x0), p(mark(x1))), MARK(x0)) A__ADD(s(x0), p(fact(z0))) -> c3(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), p(zero(z0))) -> c3(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(p(z0))) -> c3(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(add(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(s(z0))) -> c3(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(0)) -> c3(A__ADD(mark(x0), a__p(0)), MARK(x0)) A__ADD(s(x0), p(true)) -> c3(A__ADD(mark(x0), a__p(true)), MARK(x0)) A__ADD(s(x0), p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1)))) A__ADD(s(x0), add(x1, x2)) -> c3(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), add(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), add(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, p(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, s(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, 0)) -> c3(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), add(x1, true)) -> c3(A__ADD(mark(x0), a__add(mark(x1), true)), MARK(x0)) A__ADD(s(x0), add(x1, false)) -> c3(A__ADD(mark(x0), a__add(mark(x1), false)), MARK(x0)) A__ADD(s(x0), add(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), add(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(p(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(s(z0), x2)) -> c3(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(0, x2)) -> c3(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) A__ADD(s(x0), add(true, x2)) -> c3(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(x0)) A__ADD(s(x0), add(false, x2)) -> c3(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), add(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), add(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), add(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__add(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), add(x1, x2)) -> c3(A__ADD(0, a__add(mark(x1), mark(x2))), MARK(0)) A__ADD(s(true), add(x1, x2)) -> c3(A__ADD(true, a__add(mark(x1), mark(x2))), MARK(true)) A__ADD(s(false), add(x1, x2)) -> c3(A__ADD(false, a__add(mark(x1), mark(x2))), MARK(false)) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1)))) A__ADD(s(x0), prod(x1, x2)) -> c3(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), prod(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, p(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, s(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, 0)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), prod(x1, true)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(x0)) A__ADD(s(x0), prod(x1, false)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(x0)) A__ADD(s(x0), prod(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(p(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(0, x2)) -> c3(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(true, x2)) -> c3(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(false, x2)) -> c3(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), prod(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2)))) A__ADD(s(x0), p(x1)) -> c3(A__ADD(mark(x0), p(mark(x1))), MARK(x0)) A__ADD(s(x0), p(fact(z0))) -> c3(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), p(zero(z0))) -> c3(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(p(z0))) -> c3(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(add(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(s(z0))) -> c3(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(0)) -> c3(A__ADD(mark(x0), a__p(0)), MARK(x0)) A__ADD(s(x0), p(true)) -> c3(A__ADD(mark(x0), a__p(true)), MARK(x0)) A__ADD(s(x0), p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1)))) A__ADD(s(x0), add(x1, x2)) -> c3(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), add(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), add(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, p(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, s(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, 0)) -> c3(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), add(x1, true)) -> c3(A__ADD(mark(x0), a__add(mark(x1), true)), MARK(x0)) A__ADD(s(x0), add(x1, false)) -> c3(A__ADD(mark(x0), a__add(mark(x1), false)), MARK(x0)) A__ADD(s(x0), add(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), add(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(p(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(s(z0), x2)) -> c3(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(0, x2)) -> c3(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) A__ADD(s(x0), add(true, x2)) -> c3(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(x0)) A__ADD(s(x0), add(false, x2)) -> c3(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), add(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), add(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), add(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__add(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), add(x1, x2)) -> c3(A__ADD(0, a__add(mark(x1), mark(x2))), MARK(0)) A__ADD(s(true), add(x1, x2)) -> c3(A__ADD(true, a__add(mark(x1), mark(x2))), MARK(true)) A__ADD(s(false), add(x1, x2)) -> c3(A__ADD(false, a__add(mark(x1), mark(x2))), MARK(false)) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__PROD_2, A__FACT_1 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c27_1, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1, c24_2, c25_2, c25_1, c26_2, c26_1, c_2, c_1 ---------------------------------------- (157) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: A__ADD(s(true), add(x1, x2)) -> c3(A__ADD(true, a__add(mark(x1), mark(x2))), MARK(true)) A__ADD(s(false), add(x1, x2)) -> c3(A__ADD(false, a__add(mark(x1), mark(x2))), MARK(false)) ---------------------------------------- (158) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) 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x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(0, x2)) -> c3(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(true, x2)) -> c3(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(false, x2)) -> c3(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), prod(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2)))) A__ADD(s(x0), p(x1)) -> c3(A__ADD(mark(x0), p(mark(x1))), MARK(x0)) A__ADD(s(x0), p(fact(z0))) -> c3(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), p(zero(z0))) -> c3(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(p(z0))) -> c3(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(add(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(s(z0))) -> c3(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(0)) -> c3(A__ADD(mark(x0), a__p(0)), MARK(x0)) A__ADD(s(x0), p(true)) -> c3(A__ADD(mark(x0), a__p(true)), MARK(x0)) A__ADD(s(x0), p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1)))) A__ADD(s(x0), add(x1, x2)) -> c3(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), add(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), add(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, p(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, s(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, 0)) -> c3(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), add(x1, true)) -> c3(A__ADD(mark(x0), a__add(mark(x1), true)), MARK(x0)) A__ADD(s(x0), add(x1, false)) -> c3(A__ADD(mark(x0), a__add(mark(x1), false)), MARK(x0)) A__ADD(s(x0), add(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), add(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(p(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(s(z0), x2)) -> c3(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(0, x2)) -> c3(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) A__ADD(s(x0), add(true, x2)) -> c3(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(x0)) A__ADD(s(x0), add(false, x2)) -> c3(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), add(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), add(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), add(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__add(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), add(x1, x2)) -> c3(A__ADD(0, a__add(mark(x1), mark(x2))), MARK(0)) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1)))) A__ADD(s(x0), prod(x1, x2)) -> c3(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), prod(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, p(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, s(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, 0)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), prod(x1, true)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(x0)) A__ADD(s(x0), prod(x1, false)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(x0)) A__ADD(s(x0), prod(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(p(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(0, x2)) -> c3(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(true, x2)) -> c3(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(false, x2)) -> c3(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), prod(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2)))) A__ADD(s(x0), p(x1)) -> c3(A__ADD(mark(x0), p(mark(x1))), MARK(x0)) A__ADD(s(x0), p(fact(z0))) -> c3(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), p(zero(z0))) -> c3(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(p(z0))) -> c3(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(add(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(s(z0))) -> c3(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(0)) -> c3(A__ADD(mark(x0), a__p(0)), MARK(x0)) A__ADD(s(x0), p(true)) -> c3(A__ADD(mark(x0), a__p(true)), MARK(x0)) A__ADD(s(x0), p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1)))) A__ADD(s(x0), add(x1, x2)) -> c3(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), add(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), add(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, p(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, s(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, 0)) -> c3(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), add(x1, true)) -> c3(A__ADD(mark(x0), a__add(mark(x1), true)), MARK(x0)) A__ADD(s(x0), add(x1, false)) -> c3(A__ADD(mark(x0), a__add(mark(x1), false)), MARK(x0)) A__ADD(s(x0), add(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), add(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(p(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(s(z0), x2)) -> c3(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(0, x2)) -> c3(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) A__ADD(s(x0), add(true, x2)) -> c3(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(x0)) A__ADD(s(x0), add(false, x2)) -> c3(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), add(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), add(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), add(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__add(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), add(x1, x2)) -> c3(A__ADD(0, a__add(mark(x1), mark(x2))), MARK(0)) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__PROD_2, A__FACT_1 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c27_1, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1, c24_2, c25_2, c25_1, c26_2, c26_1, c_2, c_1 ---------------------------------------- (159) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (160) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1)))) A__ADD(s(x0), prod(x1, x2)) -> c3(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), prod(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, p(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, s(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, 0)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), prod(x1, true)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(x0)) A__ADD(s(x0), prod(x1, false)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(x0)) A__ADD(s(x0), prod(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(p(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(0, x2)) -> c3(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(true, x2)) -> c3(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(false, x2)) -> c3(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), prod(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2)))) A__ADD(s(x0), p(x1)) -> c3(A__ADD(mark(x0), p(mark(x1))), MARK(x0)) A__ADD(s(x0), p(fact(z0))) -> c3(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), p(zero(z0))) -> c3(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(p(z0))) -> c3(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(add(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(s(z0))) -> c3(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(0)) -> c3(A__ADD(mark(x0), a__p(0)), MARK(x0)) A__ADD(s(x0), p(true)) -> c3(A__ADD(mark(x0), a__p(true)), MARK(x0)) A__ADD(s(x0), p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1)))) A__ADD(s(x0), add(x1, x2)) -> c3(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), add(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), add(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, p(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, s(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, 0)) -> c3(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), add(x1, true)) -> c3(A__ADD(mark(x0), a__add(mark(x1), true)), MARK(x0)) A__ADD(s(x0), add(x1, false)) -> c3(A__ADD(mark(x0), a__add(mark(x1), false)), MARK(x0)) A__ADD(s(x0), add(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), add(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(p(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(s(z0), x2)) -> c3(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(0, x2)) -> c3(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) A__ADD(s(x0), add(true, x2)) -> c3(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(x0)) A__ADD(s(x0), add(false, x2)) -> c3(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), add(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), add(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), add(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__add(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), add(x1, x2)) -> c3(A__ADD(0, a__add(mark(x1), mark(x2)))) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1)))) A__ADD(s(x0), prod(x1, x2)) -> c3(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), prod(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, p(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, s(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, 0)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), prod(x1, true)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(x0)) A__ADD(s(x0), prod(x1, false)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(x0)) A__ADD(s(x0), prod(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(p(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(0, x2)) -> c3(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(true, x2)) -> c3(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(false, x2)) -> c3(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), prod(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2)))) A__ADD(s(x0), p(x1)) -> c3(A__ADD(mark(x0), p(mark(x1))), MARK(x0)) A__ADD(s(x0), p(fact(z0))) -> c3(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), p(zero(z0))) -> c3(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(p(z0))) -> c3(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(add(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(s(z0))) -> c3(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(0)) -> c3(A__ADD(mark(x0), a__p(0)), MARK(x0)) A__ADD(s(x0), p(true)) -> c3(A__ADD(mark(x0), a__p(true)), MARK(x0)) A__ADD(s(x0), p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1)))) A__ADD(s(x0), add(x1, x2)) -> c3(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), add(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), add(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, p(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, s(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, 0)) -> c3(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), add(x1, true)) -> c3(A__ADD(mark(x0), a__add(mark(x1), true)), MARK(x0)) A__ADD(s(x0), add(x1, false)) -> c3(A__ADD(mark(x0), a__add(mark(x1), false)), MARK(x0)) A__ADD(s(x0), add(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), add(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(p(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(s(z0), x2)) -> c3(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(0, x2)) -> c3(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) A__ADD(s(x0), add(true, x2)) -> c3(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(x0)) A__ADD(s(x0), add(false, x2)) -> c3(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), add(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), add(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), add(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__add(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), add(x1, x2)) -> c3(A__ADD(0, a__add(mark(x1), mark(x2)))) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__PROD_2, A__FACT_1 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c27_1, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1, c24_2, c25_2, c25_1, c26_2, c26_1, c_2, c_1 ---------------------------------------- (161) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__ADD(s(x0), s(z0)) -> c3(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) by A__ADD(s(x0), s(fact(z0))) -> c3(A__ADD(mark(x0), s(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), s(zero(z0))) -> c3(A__ADD(mark(x0), s(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(prod(z0, z1))) -> c3(A__ADD(mark(x0), s(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(p(z0))) -> c3(A__ADD(mark(x0), s(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(add(z0, z1))) -> c3(A__ADD(mark(x0), s(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(s(z0))) -> c3(A__ADD(mark(x0), s(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(0)) -> c3(A__ADD(mark(x0), s(0)), MARK(x0)) A__ADD(s(x0), s(true)) -> c3(A__ADD(mark(x0), s(true)), MARK(x0)) A__ADD(s(x0), s(false)) -> c3(A__ADD(mark(x0), s(false)), MARK(x0)) A__ADD(s(fact(z0)), s(x1)) -> c3(A__ADD(a__fact(mark(z0)), s(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), s(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), s(x1)) -> c3(A__ADD(a__zero(mark(z0)), s(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), s(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), s(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), s(x1)) -> c3(A__ADD(a__p(mark(z0)), s(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), s(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), s(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), s(x1)) -> c3(A__ADD(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__ADD(s(0), s(x1)) -> c3(A__ADD(0, s(mark(x1))), MARK(0)) A__ADD(s(true), s(x1)) -> c3(A__ADD(true, s(mark(x1))), MARK(true)) A__ADD(s(false), s(x1)) -> c3(A__ADD(false, s(mark(x1))), MARK(false)) ---------------------------------------- (162) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), 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MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1)))) A__ADD(s(x0), prod(x1, x2)) -> c3(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), prod(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, p(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, s(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, 0)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), prod(x1, true)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(x0)) A__ADD(s(x0), prod(x1, false)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(x0)) A__ADD(s(x0), prod(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(p(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(0, x2)) -> c3(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(true, x2)) -> c3(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(false, x2)) -> c3(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), prod(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2)))) A__ADD(s(x0), p(x1)) -> c3(A__ADD(mark(x0), p(mark(x1))), MARK(x0)) A__ADD(s(x0), p(fact(z0))) -> c3(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), p(zero(z0))) -> c3(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(p(z0))) -> c3(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(add(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(s(z0))) -> c3(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(0)) -> c3(A__ADD(mark(x0), a__p(0)), MARK(x0)) A__ADD(s(x0), p(true)) -> c3(A__ADD(mark(x0), a__p(true)), MARK(x0)) A__ADD(s(x0), p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1)))) A__ADD(s(x0), add(x1, x2)) -> c3(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), add(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), add(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, p(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, s(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, 0)) -> c3(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), add(x1, true)) -> c3(A__ADD(mark(x0), a__add(mark(x1), true)), MARK(x0)) A__ADD(s(x0), add(x1, false)) -> c3(A__ADD(mark(x0), a__add(mark(x1), false)), MARK(x0)) A__ADD(s(x0), add(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), add(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(p(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(s(z0), x2)) -> c3(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(0, x2)) -> c3(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) A__ADD(s(x0), add(true, x2)) -> c3(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(x0)) A__ADD(s(x0), add(false, x2)) -> c3(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), add(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), add(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), add(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__add(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), add(x1, x2)) -> c3(A__ADD(0, a__add(mark(x1), mark(x2)))) A__ADD(s(x0), s(fact(z0))) -> c3(A__ADD(mark(x0), s(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), s(zero(z0))) -> c3(A__ADD(mark(x0), s(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(prod(z0, z1))) -> c3(A__ADD(mark(x0), s(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(p(z0))) -> c3(A__ADD(mark(x0), s(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(add(z0, z1))) -> c3(A__ADD(mark(x0), s(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(s(z0))) -> c3(A__ADD(mark(x0), s(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(0)) -> c3(A__ADD(mark(x0), s(0)), MARK(x0)) A__ADD(s(x0), s(true)) -> c3(A__ADD(mark(x0), s(true)), MARK(x0)) A__ADD(s(x0), s(false)) -> c3(A__ADD(mark(x0), s(false)), MARK(x0)) A__ADD(s(fact(z0)), s(x1)) -> c3(A__ADD(a__fact(mark(z0)), s(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), s(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), s(x1)) -> c3(A__ADD(a__zero(mark(z0)), s(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), s(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), s(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), s(x1)) -> c3(A__ADD(a__p(mark(z0)), s(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), s(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), s(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), s(x1)) -> c3(A__ADD(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__ADD(s(0), s(x1)) -> c3(A__ADD(0, s(mark(x1))), MARK(0)) A__ADD(s(true), s(x1)) -> c3(A__ADD(true, s(mark(x1))), MARK(true)) A__ADD(s(false), s(x1)) -> c3(A__ADD(false, s(mark(x1))), MARK(false)) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> 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A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1)))) A__ADD(s(x0), prod(x1, x2)) -> c3(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), prod(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, p(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, s(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, 0)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), prod(x1, true)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(x0)) A__ADD(s(x0), prod(x1, false)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(x0)) A__ADD(s(x0), prod(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(p(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(0, x2)) -> c3(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(true, x2)) -> c3(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(false, x2)) -> c3(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), prod(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2)))) A__ADD(s(x0), p(x1)) -> c3(A__ADD(mark(x0), p(mark(x1))), MARK(x0)) A__ADD(s(x0), p(fact(z0))) -> c3(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), p(zero(z0))) -> c3(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(p(z0))) -> c3(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(add(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(s(z0))) -> c3(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(0)) -> c3(A__ADD(mark(x0), a__p(0)), MARK(x0)) A__ADD(s(x0), p(true)) -> c3(A__ADD(mark(x0), a__p(true)), MARK(x0)) A__ADD(s(x0), p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1)))) A__ADD(s(x0), add(x1, x2)) -> c3(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), add(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), add(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, p(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, s(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, 0)) -> c3(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), add(x1, true)) -> c3(A__ADD(mark(x0), a__add(mark(x1), true)), MARK(x0)) A__ADD(s(x0), add(x1, false)) -> c3(A__ADD(mark(x0), a__add(mark(x1), false)), MARK(x0)) A__ADD(s(x0), add(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), add(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(p(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(s(z0), x2)) -> c3(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(0, x2)) -> c3(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) A__ADD(s(x0), add(true, x2)) -> c3(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(x0)) A__ADD(s(x0), add(false, x2)) -> c3(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), add(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), add(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), add(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__add(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), add(x1, x2)) -> c3(A__ADD(0, a__add(mark(x1), mark(x2)))) A__ADD(s(x0), s(fact(z0))) -> c3(A__ADD(mark(x0), s(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), s(zero(z0))) -> c3(A__ADD(mark(x0), s(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(prod(z0, z1))) -> c3(A__ADD(mark(x0), s(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(p(z0))) -> c3(A__ADD(mark(x0), s(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(add(z0, z1))) -> c3(A__ADD(mark(x0), s(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(s(z0))) -> c3(A__ADD(mark(x0), s(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(0)) -> c3(A__ADD(mark(x0), s(0)), MARK(x0)) A__ADD(s(x0), s(true)) -> c3(A__ADD(mark(x0), s(true)), MARK(x0)) A__ADD(s(x0), s(false)) -> c3(A__ADD(mark(x0), s(false)), MARK(x0)) A__ADD(s(fact(z0)), s(x1)) -> c3(A__ADD(a__fact(mark(z0)), s(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), s(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), s(x1)) -> c3(A__ADD(a__zero(mark(z0)), s(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), s(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), s(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), s(x1)) -> c3(A__ADD(a__p(mark(z0)), s(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), s(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), s(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), s(x1)) -> c3(A__ADD(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__ADD(s(0), s(x1)) -> c3(A__ADD(0, s(mark(x1))), MARK(0)) A__ADD(s(true), s(x1)) -> c3(A__ADD(true, s(mark(x1))), MARK(true)) A__ADD(s(false), s(x1)) -> c3(A__ADD(false, s(mark(x1))), MARK(false)) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__PROD_2, A__FACT_1 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c27_1, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1, c24_2, c25_2, c25_1, c26_2, c26_1, c_2, c_1 ---------------------------------------- (163) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: A__ADD(s(false), s(x1)) -> c3(A__ADD(false, s(mark(x1))), MARK(false)) A__ADD(s(true), s(x1)) -> c3(A__ADD(true, s(mark(x1))), MARK(true)) ---------------------------------------- (164) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1)))) A__ADD(s(x0), prod(x1, x2)) -> c3(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), prod(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, p(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, s(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, 0)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), prod(x1, true)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(x0)) A__ADD(s(x0), prod(x1, false)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(x0)) A__ADD(s(x0), prod(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(p(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(0, x2)) -> c3(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(true, x2)) -> c3(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(false, x2)) -> c3(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), prod(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2)))) A__ADD(s(x0), p(x1)) -> c3(A__ADD(mark(x0), p(mark(x1))), MARK(x0)) A__ADD(s(x0), p(fact(z0))) -> c3(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), p(zero(z0))) -> c3(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(p(z0))) -> c3(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(add(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(s(z0))) -> c3(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(0)) -> c3(A__ADD(mark(x0), a__p(0)), MARK(x0)) A__ADD(s(x0), p(true)) -> c3(A__ADD(mark(x0), a__p(true)), MARK(x0)) A__ADD(s(x0), p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1)))) A__ADD(s(x0), add(x1, x2)) -> c3(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), add(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), add(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, p(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, s(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, 0)) -> c3(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), add(x1, true)) -> c3(A__ADD(mark(x0), a__add(mark(x1), true)), MARK(x0)) A__ADD(s(x0), add(x1, false)) -> c3(A__ADD(mark(x0), a__add(mark(x1), false)), MARK(x0)) A__ADD(s(x0), add(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), add(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(p(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(s(z0), x2)) -> c3(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(0, x2)) -> c3(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) A__ADD(s(x0), add(true, x2)) -> c3(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(x0)) A__ADD(s(x0), add(false, x2)) -> c3(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), add(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), add(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), add(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__add(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), add(x1, x2)) -> c3(A__ADD(0, a__add(mark(x1), mark(x2)))) A__ADD(s(x0), s(fact(z0))) -> c3(A__ADD(mark(x0), s(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), s(zero(z0))) -> c3(A__ADD(mark(x0), s(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(prod(z0, z1))) -> c3(A__ADD(mark(x0), s(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(p(z0))) -> c3(A__ADD(mark(x0), s(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(add(z0, z1))) -> c3(A__ADD(mark(x0), s(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(s(z0))) -> c3(A__ADD(mark(x0), s(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(0)) -> c3(A__ADD(mark(x0), s(0)), MARK(x0)) A__ADD(s(x0), s(true)) -> c3(A__ADD(mark(x0), s(true)), MARK(x0)) A__ADD(s(x0), s(false)) -> c3(A__ADD(mark(x0), s(false)), MARK(x0)) A__ADD(s(fact(z0)), s(x1)) -> c3(A__ADD(a__fact(mark(z0)), s(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), s(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), s(x1)) -> c3(A__ADD(a__zero(mark(z0)), s(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), s(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), s(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), s(x1)) -> c3(A__ADD(a__p(mark(z0)), s(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), s(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), s(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), s(x1)) -> c3(A__ADD(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__ADD(s(0), s(x1)) -> c3(A__ADD(0, s(mark(x1))), MARK(0)) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, 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a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), 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MARK(x0)) A__ADD(s(x0), prod(false, x2)) -> c3(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), prod(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2)))) A__ADD(s(x0), p(x1)) -> c3(A__ADD(mark(x0), p(mark(x1))), MARK(x0)) A__ADD(s(x0), p(fact(z0))) -> c3(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), p(zero(z0))) -> c3(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(p(z0))) -> c3(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(add(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(s(z0))) -> c3(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(0)) -> c3(A__ADD(mark(x0), a__p(0)), MARK(x0)) A__ADD(s(x0), p(true)) -> c3(A__ADD(mark(x0), a__p(true)), MARK(x0)) A__ADD(s(x0), p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1)))) A__ADD(s(x0), add(x1, x2)) -> c3(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), add(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), add(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, p(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, s(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, 0)) -> c3(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), add(x1, true)) -> c3(A__ADD(mark(x0), a__add(mark(x1), true)), MARK(x0)) A__ADD(s(x0), add(x1, false)) -> c3(A__ADD(mark(x0), a__add(mark(x1), false)), MARK(x0)) A__ADD(s(x0), add(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), add(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(p(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(s(z0), x2)) -> c3(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(0, x2)) -> c3(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) A__ADD(s(x0), add(true, x2)) -> c3(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(x0)) A__ADD(s(x0), add(false, x2)) -> c3(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), add(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), add(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), add(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__add(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), add(x1, x2)) -> c3(A__ADD(0, a__add(mark(x1), mark(x2)))) A__ADD(s(x0), s(fact(z0))) -> c3(A__ADD(mark(x0), s(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), s(zero(z0))) -> c3(A__ADD(mark(x0), s(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(prod(z0, z1))) -> c3(A__ADD(mark(x0), s(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(p(z0))) -> c3(A__ADD(mark(x0), s(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(add(z0, z1))) -> c3(A__ADD(mark(x0), s(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(s(z0))) -> c3(A__ADD(mark(x0), s(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(0)) -> c3(A__ADD(mark(x0), s(0)), MARK(x0)) A__ADD(s(x0), s(true)) -> c3(A__ADD(mark(x0), s(true)), MARK(x0)) A__ADD(s(x0), s(false)) -> c3(A__ADD(mark(x0), s(false)), MARK(x0)) A__ADD(s(fact(z0)), s(x1)) -> c3(A__ADD(a__fact(mark(z0)), s(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), s(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), s(x1)) -> c3(A__ADD(a__zero(mark(z0)), s(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), s(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), s(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), s(x1)) -> c3(A__ADD(a__p(mark(z0)), s(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), s(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), s(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), s(x1)) -> c3(A__ADD(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__ADD(s(0), s(x1)) -> c3(A__ADD(0, s(mark(x1))), MARK(0)) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__PROD_2, A__FACT_1 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c27_1, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1, c24_2, c25_2, c25_1, c26_2, c26_1, c_2, c_1 ---------------------------------------- (165) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (166) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), 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A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), 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x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2)))) A__ADD(s(x0), p(x1)) -> c3(A__ADD(mark(x0), p(mark(x1))), MARK(x0)) A__ADD(s(x0), p(fact(z0))) -> c3(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), p(zero(z0))) -> c3(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(p(z0))) -> c3(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(add(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(s(z0))) -> c3(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(0)) -> c3(A__ADD(mark(x0), a__p(0)), MARK(x0)) A__ADD(s(x0), p(true)) -> c3(A__ADD(mark(x0), a__p(true)), MARK(x0)) A__ADD(s(x0), p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1)))) A__ADD(s(x0), add(x1, x2)) -> c3(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), add(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), add(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, p(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, s(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, 0)) -> c3(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), add(x1, true)) -> c3(A__ADD(mark(x0), a__add(mark(x1), true)), MARK(x0)) A__ADD(s(x0), add(x1, false)) -> c3(A__ADD(mark(x0), a__add(mark(x1), false)), MARK(x0)) A__ADD(s(x0), add(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), add(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(p(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(s(z0), x2)) -> c3(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(0, x2)) -> c3(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) A__ADD(s(x0), add(true, x2)) -> c3(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(x0)) A__ADD(s(x0), add(false, x2)) -> c3(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), add(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), add(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), add(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__add(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), add(x1, x2)) -> c3(A__ADD(0, a__add(mark(x1), mark(x2)))) A__ADD(s(x0), s(fact(z0))) -> c3(A__ADD(mark(x0), s(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), s(zero(z0))) -> c3(A__ADD(mark(x0), s(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(prod(z0, z1))) -> c3(A__ADD(mark(x0), s(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(p(z0))) -> c3(A__ADD(mark(x0), s(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(add(z0, z1))) -> c3(A__ADD(mark(x0), s(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(s(z0))) -> c3(A__ADD(mark(x0), s(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(0)) -> c3(A__ADD(mark(x0), s(0)), MARK(x0)) A__ADD(s(x0), s(true)) -> c3(A__ADD(mark(x0), s(true)), MARK(x0)) A__ADD(s(x0), s(false)) -> c3(A__ADD(mark(x0), s(false)), MARK(x0)) A__ADD(s(fact(z0)), s(x1)) -> c3(A__ADD(a__fact(mark(z0)), s(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), s(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), s(x1)) -> c3(A__ADD(a__zero(mark(z0)), s(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), s(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), s(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), s(x1)) -> c3(A__ADD(a__p(mark(z0)), s(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), s(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), s(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), s(x1)) -> c3(A__ADD(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__ADD(s(0), s(x1)) -> c3(A__ADD(0, s(mark(x1)))) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), 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z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2)))) A__ADD(s(x0), p(x1)) -> c3(A__ADD(mark(x0), p(mark(x1))), MARK(x0)) A__ADD(s(x0), p(fact(z0))) -> c3(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), p(zero(z0))) -> c3(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(p(z0))) -> c3(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(add(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(s(z0))) -> c3(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(0)) -> c3(A__ADD(mark(x0), a__p(0)), MARK(x0)) A__ADD(s(x0), p(true)) -> c3(A__ADD(mark(x0), a__p(true)), MARK(x0)) A__ADD(s(x0), p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1)))) A__ADD(s(x0), add(x1, x2)) -> c3(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), add(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), add(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, p(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, s(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, 0)) -> c3(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), add(x1, true)) -> c3(A__ADD(mark(x0), a__add(mark(x1), true)), MARK(x0)) A__ADD(s(x0), add(x1, false)) -> c3(A__ADD(mark(x0), a__add(mark(x1), false)), MARK(x0)) A__ADD(s(x0), add(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), add(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(p(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(s(z0), x2)) -> c3(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(0, x2)) -> c3(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) A__ADD(s(x0), add(true, x2)) -> c3(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(x0)) A__ADD(s(x0), add(false, x2)) -> c3(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), add(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), add(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), add(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__add(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), add(x1, x2)) -> c3(A__ADD(0, a__add(mark(x1), mark(x2)))) A__ADD(s(x0), s(fact(z0))) -> c3(A__ADD(mark(x0), s(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), s(zero(z0))) -> c3(A__ADD(mark(x0), s(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(prod(z0, z1))) -> c3(A__ADD(mark(x0), s(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(p(z0))) -> c3(A__ADD(mark(x0), s(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(add(z0, z1))) -> c3(A__ADD(mark(x0), s(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(s(z0))) -> c3(A__ADD(mark(x0), s(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(0)) -> c3(A__ADD(mark(x0), s(0)), MARK(x0)) A__ADD(s(x0), s(true)) -> c3(A__ADD(mark(x0), s(true)), MARK(x0)) A__ADD(s(x0), s(false)) -> c3(A__ADD(mark(x0), s(false)), MARK(x0)) A__ADD(s(fact(z0)), s(x1)) -> c3(A__ADD(a__fact(mark(z0)), s(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), s(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), s(x1)) -> c3(A__ADD(a__zero(mark(z0)), s(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), s(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), s(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), s(x1)) -> c3(A__ADD(a__p(mark(z0)), s(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), s(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), s(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), s(x1)) -> c3(A__ADD(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__ADD(s(0), s(x1)) -> c3(A__ADD(0, s(mark(x1)))) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__PROD_2, A__FACT_1 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c27_1, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1, c24_2, c25_2, c25_1, c26_2, c26_1, c_2, c_1 ---------------------------------------- (167) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__ADD(s(x0), 0) -> c3(A__ADD(mark(x0), 0), MARK(x0)) by A__ADD(s(fact(z0)), 0) -> c3(A__ADD(a__fact(mark(z0)), 0), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), 0) -> c3(A__ADD(a__if(mark(z0), z1, z2), 0), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), 0) -> c3(A__ADD(a__zero(mark(z0)), 0), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), 0) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), 0), MARK(prod(z0, z1))) A__ADD(s(p(z0)), 0) -> c3(A__ADD(a__p(mark(z0)), 0), MARK(p(z0))) A__ADD(s(add(z0, z1)), 0) -> c3(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) A__ADD(s(s(z0)), 0) -> c3(A__ADD(s(mark(z0)), 0), MARK(s(z0))) A__ADD(s(0), 0) -> c3(A__ADD(0, 0), MARK(0)) A__ADD(s(true), 0) -> c3(A__ADD(true, 0), MARK(true)) A__ADD(s(false), 0) -> c3(A__ADD(false, 0), MARK(false)) ---------------------------------------- (168) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), 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A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), 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x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2)))) A__ADD(s(x0), p(x1)) -> c3(A__ADD(mark(x0), p(mark(x1))), MARK(x0)) A__ADD(s(x0), p(fact(z0))) -> c3(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), p(zero(z0))) -> c3(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(p(z0))) -> c3(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(add(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(s(z0))) -> c3(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(0)) -> c3(A__ADD(mark(x0), a__p(0)), MARK(x0)) A__ADD(s(x0), p(true)) -> c3(A__ADD(mark(x0), a__p(true)), MARK(x0)) A__ADD(s(x0), p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1)))) A__ADD(s(x0), add(x1, x2)) -> c3(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), add(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), add(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, p(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, s(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, 0)) -> c3(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), add(x1, true)) -> c3(A__ADD(mark(x0), a__add(mark(x1), true)), MARK(x0)) A__ADD(s(x0), add(x1, false)) -> c3(A__ADD(mark(x0), a__add(mark(x1), false)), MARK(x0)) A__ADD(s(x0), add(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), add(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(p(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(s(z0), x2)) -> c3(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(0, x2)) -> c3(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) A__ADD(s(x0), add(true, x2)) -> c3(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(x0)) A__ADD(s(x0), add(false, x2)) -> c3(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), add(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), add(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), add(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__add(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), add(x1, x2)) -> c3(A__ADD(0, a__add(mark(x1), mark(x2)))) A__ADD(s(x0), s(fact(z0))) -> c3(A__ADD(mark(x0), s(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), s(zero(z0))) -> c3(A__ADD(mark(x0), s(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(prod(z0, z1))) -> c3(A__ADD(mark(x0), s(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(p(z0))) -> c3(A__ADD(mark(x0), s(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(add(z0, z1))) -> c3(A__ADD(mark(x0), s(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(s(z0))) -> c3(A__ADD(mark(x0), s(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(0)) -> c3(A__ADD(mark(x0), s(0)), MARK(x0)) A__ADD(s(x0), s(true)) -> c3(A__ADD(mark(x0), s(true)), MARK(x0)) A__ADD(s(x0), s(false)) -> c3(A__ADD(mark(x0), s(false)), MARK(x0)) A__ADD(s(fact(z0)), s(x1)) -> c3(A__ADD(a__fact(mark(z0)), s(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), s(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), s(x1)) -> c3(A__ADD(a__zero(mark(z0)), s(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), s(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), s(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), s(x1)) -> c3(A__ADD(a__p(mark(z0)), s(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), s(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), s(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), s(x1)) -> c3(A__ADD(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__ADD(s(0), s(x1)) -> c3(A__ADD(0, s(mark(x1)))) A__ADD(s(fact(z0)), 0) -> c3(A__ADD(a__fact(mark(z0)), 0), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), 0) -> c3(A__ADD(a__if(mark(z0), z1, z2), 0), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), 0) -> c3(A__ADD(a__zero(mark(z0)), 0), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), 0) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), 0), MARK(prod(z0, z1))) A__ADD(s(p(z0)), 0) -> c3(A__ADD(a__p(mark(z0)), 0), MARK(p(z0))) A__ADD(s(add(z0, z1)), 0) -> c3(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) A__ADD(s(s(z0)), 0) -> c3(A__ADD(s(mark(z0)), 0), MARK(s(z0))) A__ADD(s(0), 0) -> c3(A__ADD(0, 0), MARK(0)) A__ADD(s(true), 0) -> c3(A__ADD(true, 0), MARK(true)) A__ADD(s(false), 0) -> c3(A__ADD(false, 0), MARK(false)) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1)))) A__ADD(s(x0), prod(x1, x2)) -> c3(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), prod(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, p(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, s(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, 0)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), prod(x1, true)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(x0)) A__ADD(s(x0), prod(x1, false)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(x0)) A__ADD(s(x0), prod(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(p(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(0, x2)) -> c3(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(true, x2)) -> c3(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(false, x2)) -> c3(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), prod(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2)))) A__ADD(s(x0), p(x1)) -> c3(A__ADD(mark(x0), p(mark(x1))), MARK(x0)) A__ADD(s(x0), p(fact(z0))) -> c3(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), p(zero(z0))) -> c3(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(p(z0))) -> c3(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(add(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(s(z0))) -> c3(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(0)) -> c3(A__ADD(mark(x0), a__p(0)), MARK(x0)) A__ADD(s(x0), p(true)) -> c3(A__ADD(mark(x0), a__p(true)), MARK(x0)) A__ADD(s(x0), p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1)))) A__ADD(s(x0), add(x1, x2)) -> c3(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), add(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), add(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, p(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, s(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, 0)) -> c3(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), add(x1, true)) -> c3(A__ADD(mark(x0), a__add(mark(x1), true)), MARK(x0)) A__ADD(s(x0), add(x1, false)) -> c3(A__ADD(mark(x0), a__add(mark(x1), false)), MARK(x0)) A__ADD(s(x0), add(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), add(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(p(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(s(z0), x2)) -> c3(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(0, x2)) -> c3(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) A__ADD(s(x0), add(true, x2)) -> c3(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(x0)) A__ADD(s(x0), add(false, x2)) -> c3(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), add(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), add(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), add(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__add(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), add(x1, x2)) -> c3(A__ADD(0, a__add(mark(x1), mark(x2)))) A__ADD(s(x0), s(fact(z0))) -> c3(A__ADD(mark(x0), s(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), s(zero(z0))) -> c3(A__ADD(mark(x0), s(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(prod(z0, z1))) -> c3(A__ADD(mark(x0), s(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(p(z0))) -> c3(A__ADD(mark(x0), s(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(add(z0, z1))) -> c3(A__ADD(mark(x0), s(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(s(z0))) -> c3(A__ADD(mark(x0), s(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(0)) -> c3(A__ADD(mark(x0), s(0)), MARK(x0)) A__ADD(s(x0), s(true)) -> c3(A__ADD(mark(x0), s(true)), MARK(x0)) A__ADD(s(x0), s(false)) -> c3(A__ADD(mark(x0), s(false)), MARK(x0)) A__ADD(s(fact(z0)), s(x1)) -> c3(A__ADD(a__fact(mark(z0)), s(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), s(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), s(x1)) -> c3(A__ADD(a__zero(mark(z0)), s(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), s(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), s(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), s(x1)) -> c3(A__ADD(a__p(mark(z0)), s(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), s(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), s(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), s(x1)) -> c3(A__ADD(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__ADD(s(0), s(x1)) -> c3(A__ADD(0, s(mark(x1)))) A__ADD(s(fact(z0)), 0) -> c3(A__ADD(a__fact(mark(z0)), 0), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), 0) -> c3(A__ADD(a__if(mark(z0), z1, z2), 0), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), 0) -> c3(A__ADD(a__zero(mark(z0)), 0), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), 0) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), 0), MARK(prod(z0, z1))) A__ADD(s(p(z0)), 0) -> c3(A__ADD(a__p(mark(z0)), 0), MARK(p(z0))) A__ADD(s(add(z0, z1)), 0) -> c3(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) A__ADD(s(s(z0)), 0) -> c3(A__ADD(s(mark(z0)), 0), MARK(s(z0))) A__ADD(s(0), 0) -> c3(A__ADD(0, 0), MARK(0)) A__ADD(s(true), 0) -> c3(A__ADD(true, 0), MARK(true)) A__ADD(s(false), 0) -> c3(A__ADD(false, 0), MARK(false)) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__PROD_2, A__FACT_1 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c27_1, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1, c24_2, c25_2, c25_1, c26_2, c26_1, c_2, c_1 ---------------------------------------- (169) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: A__ADD(s(false), 0) -> c3(A__ADD(false, 0), MARK(false)) A__ADD(s(true), 0) -> c3(A__ADD(true, 0), MARK(true)) ---------------------------------------- (170) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), 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mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(p(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(0, x2)) -> c3(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(true, x2)) -> c3(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(false, x2)) -> c3(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), prod(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2)))) A__ADD(s(x0), p(x1)) -> c3(A__ADD(mark(x0), p(mark(x1))), MARK(x0)) A__ADD(s(x0), p(fact(z0))) -> c3(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), p(zero(z0))) -> c3(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(p(z0))) -> c3(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(add(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(s(z0))) -> c3(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(0)) -> c3(A__ADD(mark(x0), a__p(0)), MARK(x0)) A__ADD(s(x0), p(true)) -> c3(A__ADD(mark(x0), a__p(true)), MARK(x0)) A__ADD(s(x0), p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1)))) A__ADD(s(x0), add(x1, x2)) -> c3(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), add(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), add(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, p(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, s(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, 0)) -> c3(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), add(x1, true)) -> c3(A__ADD(mark(x0), a__add(mark(x1), true)), MARK(x0)) A__ADD(s(x0), add(x1, false)) -> c3(A__ADD(mark(x0), a__add(mark(x1), false)), MARK(x0)) A__ADD(s(x0), add(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), add(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(p(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(s(z0), x2)) -> c3(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(0, x2)) -> c3(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) A__ADD(s(x0), add(true, x2)) -> c3(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(x0)) A__ADD(s(x0), add(false, x2)) -> c3(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), add(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), add(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), add(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__add(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), add(x1, x2)) -> c3(A__ADD(0, a__add(mark(x1), mark(x2)))) A__ADD(s(x0), s(fact(z0))) -> c3(A__ADD(mark(x0), s(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), s(zero(z0))) -> c3(A__ADD(mark(x0), s(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(prod(z0, z1))) -> c3(A__ADD(mark(x0), s(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(p(z0))) -> c3(A__ADD(mark(x0), s(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(add(z0, z1))) -> c3(A__ADD(mark(x0), s(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(s(z0))) -> c3(A__ADD(mark(x0), s(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(0)) -> c3(A__ADD(mark(x0), s(0)), MARK(x0)) A__ADD(s(x0), s(true)) -> c3(A__ADD(mark(x0), s(true)), MARK(x0)) A__ADD(s(x0), s(false)) -> c3(A__ADD(mark(x0), s(false)), MARK(x0)) A__ADD(s(fact(z0)), s(x1)) -> c3(A__ADD(a__fact(mark(z0)), s(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), s(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), s(x1)) -> c3(A__ADD(a__zero(mark(z0)), s(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), s(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), s(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), s(x1)) -> c3(A__ADD(a__p(mark(z0)), s(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), s(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), s(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), s(x1)) -> c3(A__ADD(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__ADD(s(0), s(x1)) -> c3(A__ADD(0, s(mark(x1)))) A__ADD(s(fact(z0)), 0) -> c3(A__ADD(a__fact(mark(z0)), 0), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), 0) -> c3(A__ADD(a__if(mark(z0), z1, z2), 0), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), 0) -> c3(A__ADD(a__zero(mark(z0)), 0), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), 0) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), 0), MARK(prod(z0, z1))) A__ADD(s(p(z0)), 0) -> c3(A__ADD(a__p(mark(z0)), 0), MARK(p(z0))) A__ADD(s(add(z0, z1)), 0) -> c3(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) A__ADD(s(s(z0)), 0) -> c3(A__ADD(s(mark(z0)), 0), MARK(s(z0))) A__ADD(s(0), 0) -> c3(A__ADD(0, 0), MARK(0)) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1)))) A__ADD(s(x0), prod(x1, x2)) -> c3(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), prod(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, p(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, s(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, 0)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), prod(x1, true)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(x0)) A__ADD(s(x0), prod(x1, false)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(x0)) A__ADD(s(x0), prod(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(p(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(0, x2)) -> c3(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(true, x2)) -> c3(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(false, x2)) -> c3(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), prod(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2)))) A__ADD(s(x0), p(x1)) -> c3(A__ADD(mark(x0), p(mark(x1))), MARK(x0)) A__ADD(s(x0), p(fact(z0))) -> c3(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), p(zero(z0))) -> c3(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(p(z0))) -> c3(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(add(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(s(z0))) -> c3(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(0)) -> c3(A__ADD(mark(x0), a__p(0)), MARK(x0)) A__ADD(s(x0), p(true)) -> c3(A__ADD(mark(x0), a__p(true)), MARK(x0)) A__ADD(s(x0), p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1)))) A__ADD(s(x0), add(x1, x2)) -> c3(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), add(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), add(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, p(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, s(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, 0)) -> c3(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), add(x1, true)) -> c3(A__ADD(mark(x0), a__add(mark(x1), true)), MARK(x0)) A__ADD(s(x0), add(x1, false)) -> c3(A__ADD(mark(x0), a__add(mark(x1), false)), MARK(x0)) A__ADD(s(x0), add(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), add(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(p(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(s(z0), x2)) -> c3(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(0, x2)) -> c3(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) A__ADD(s(x0), add(true, x2)) -> c3(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(x0)) A__ADD(s(x0), add(false, x2)) -> c3(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), add(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), add(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), add(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__add(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), add(x1, x2)) -> c3(A__ADD(0, a__add(mark(x1), mark(x2)))) A__ADD(s(x0), s(fact(z0))) -> c3(A__ADD(mark(x0), s(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), s(zero(z0))) -> c3(A__ADD(mark(x0), s(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(prod(z0, z1))) -> c3(A__ADD(mark(x0), s(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(p(z0))) -> c3(A__ADD(mark(x0), s(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(add(z0, z1))) -> c3(A__ADD(mark(x0), s(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(s(z0))) -> c3(A__ADD(mark(x0), s(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(0)) -> c3(A__ADD(mark(x0), s(0)), MARK(x0)) A__ADD(s(x0), s(true)) -> c3(A__ADD(mark(x0), s(true)), MARK(x0)) A__ADD(s(x0), s(false)) -> c3(A__ADD(mark(x0), s(false)), MARK(x0)) A__ADD(s(fact(z0)), s(x1)) -> c3(A__ADD(a__fact(mark(z0)), s(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), s(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), s(x1)) -> c3(A__ADD(a__zero(mark(z0)), s(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), s(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), s(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), s(x1)) -> c3(A__ADD(a__p(mark(z0)), s(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), s(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), s(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), s(x1)) -> c3(A__ADD(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__ADD(s(0), s(x1)) -> c3(A__ADD(0, s(mark(x1)))) A__ADD(s(fact(z0)), 0) -> c3(A__ADD(a__fact(mark(z0)), 0), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), 0) -> c3(A__ADD(a__if(mark(z0), z1, z2), 0), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), 0) -> c3(A__ADD(a__zero(mark(z0)), 0), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), 0) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), 0), MARK(prod(z0, z1))) A__ADD(s(p(z0)), 0) -> c3(A__ADD(a__p(mark(z0)), 0), MARK(p(z0))) A__ADD(s(add(z0, z1)), 0) -> c3(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) A__ADD(s(s(z0)), 0) -> c3(A__ADD(s(mark(z0)), 0), MARK(s(z0))) A__ADD(s(0), 0) -> c3(A__ADD(0, 0), MARK(0)) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__PROD_2, A__FACT_1 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c27_1, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1, c24_2, c25_2, c25_1, c26_2, c26_1, c_2, c_1 ---------------------------------------- (171) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (172) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), 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A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), 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x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2)))) A__ADD(s(x0), p(x1)) -> c3(A__ADD(mark(x0), p(mark(x1))), MARK(x0)) A__ADD(s(x0), p(fact(z0))) -> c3(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), p(zero(z0))) -> c3(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(p(z0))) -> c3(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(add(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(s(z0))) -> c3(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(0)) -> c3(A__ADD(mark(x0), a__p(0)), MARK(x0)) A__ADD(s(x0), p(true)) -> c3(A__ADD(mark(x0), a__p(true)), MARK(x0)) A__ADD(s(x0), p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1)))) A__ADD(s(x0), add(x1, x2)) -> c3(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), add(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), add(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, p(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, s(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, 0)) -> c3(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), add(x1, true)) -> c3(A__ADD(mark(x0), a__add(mark(x1), true)), MARK(x0)) A__ADD(s(x0), add(x1, false)) -> c3(A__ADD(mark(x0), a__add(mark(x1), false)), MARK(x0)) A__ADD(s(x0), add(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), add(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(p(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(s(z0), x2)) -> c3(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(0, x2)) -> c3(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) A__ADD(s(x0), add(true, x2)) -> c3(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(x0)) A__ADD(s(x0), add(false, x2)) -> c3(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), add(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), add(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), add(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__add(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), add(x1, x2)) -> c3(A__ADD(0, a__add(mark(x1), mark(x2)))) A__ADD(s(x0), s(fact(z0))) -> c3(A__ADD(mark(x0), s(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), s(zero(z0))) -> c3(A__ADD(mark(x0), s(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(prod(z0, z1))) -> c3(A__ADD(mark(x0), s(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(p(z0))) -> c3(A__ADD(mark(x0), s(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(add(z0, z1))) -> c3(A__ADD(mark(x0), s(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(s(z0))) -> c3(A__ADD(mark(x0), s(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(0)) -> c3(A__ADD(mark(x0), s(0)), MARK(x0)) A__ADD(s(x0), s(true)) -> c3(A__ADD(mark(x0), s(true)), MARK(x0)) A__ADD(s(x0), s(false)) -> c3(A__ADD(mark(x0), s(false)), MARK(x0)) A__ADD(s(fact(z0)), s(x1)) -> c3(A__ADD(a__fact(mark(z0)), s(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), s(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), s(x1)) -> c3(A__ADD(a__zero(mark(z0)), s(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), s(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), s(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), s(x1)) -> c3(A__ADD(a__p(mark(z0)), s(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), s(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), s(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), s(x1)) -> c3(A__ADD(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__ADD(s(0), s(x1)) -> c3(A__ADD(0, s(mark(x1)))) A__ADD(s(fact(z0)), 0) -> c3(A__ADD(a__fact(mark(z0)), 0), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), 0) -> c3(A__ADD(a__if(mark(z0), z1, z2), 0), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), 0) -> c3(A__ADD(a__zero(mark(z0)), 0), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), 0) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), 0), MARK(prod(z0, z1))) A__ADD(s(p(z0)), 0) -> c3(A__ADD(a__p(mark(z0)), 0), MARK(p(z0))) A__ADD(s(add(z0, z1)), 0) -> c3(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) A__ADD(s(s(z0)), 0) -> c3(A__ADD(s(mark(z0)), 0), MARK(s(z0))) A__ADD(s(0), 0) -> c3(A__ADD(0, 0)) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1)))) A__ADD(s(x0), prod(x1, x2)) -> c3(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), prod(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, p(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, s(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, 0)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), prod(x1, true)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(x0)) A__ADD(s(x0), prod(x1, false)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(x0)) A__ADD(s(x0), prod(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(p(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(0, x2)) -> c3(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(true, x2)) -> c3(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(false, x2)) -> c3(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), prod(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2)))) A__ADD(s(x0), p(x1)) -> c3(A__ADD(mark(x0), p(mark(x1))), MARK(x0)) A__ADD(s(x0), p(fact(z0))) -> c3(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), p(zero(z0))) -> c3(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(p(z0))) -> c3(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(add(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(s(z0))) -> c3(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(0)) -> c3(A__ADD(mark(x0), a__p(0)), MARK(x0)) A__ADD(s(x0), p(true)) -> c3(A__ADD(mark(x0), a__p(true)), MARK(x0)) A__ADD(s(x0), p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1)))) A__ADD(s(x0), add(x1, x2)) -> c3(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), add(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), add(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, p(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, s(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, 0)) -> c3(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), add(x1, true)) -> c3(A__ADD(mark(x0), a__add(mark(x1), true)), MARK(x0)) A__ADD(s(x0), add(x1, false)) -> c3(A__ADD(mark(x0), a__add(mark(x1), false)), MARK(x0)) A__ADD(s(x0), add(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), add(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(p(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(s(z0), x2)) -> c3(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(0, x2)) -> c3(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) A__ADD(s(x0), add(true, x2)) -> c3(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(x0)) A__ADD(s(x0), add(false, x2)) -> c3(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), add(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), add(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), add(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__add(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), add(x1, x2)) -> c3(A__ADD(0, a__add(mark(x1), mark(x2)))) A__ADD(s(x0), s(fact(z0))) -> c3(A__ADD(mark(x0), s(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), s(zero(z0))) -> c3(A__ADD(mark(x0), s(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(prod(z0, z1))) -> c3(A__ADD(mark(x0), s(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(p(z0))) -> c3(A__ADD(mark(x0), s(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(add(z0, z1))) -> c3(A__ADD(mark(x0), s(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(s(z0))) -> c3(A__ADD(mark(x0), s(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(0)) -> c3(A__ADD(mark(x0), s(0)), MARK(x0)) A__ADD(s(x0), s(true)) -> c3(A__ADD(mark(x0), s(true)), MARK(x0)) A__ADD(s(x0), s(false)) -> c3(A__ADD(mark(x0), s(false)), MARK(x0)) A__ADD(s(fact(z0)), s(x1)) -> c3(A__ADD(a__fact(mark(z0)), s(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), s(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), s(x1)) -> c3(A__ADD(a__zero(mark(z0)), s(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), s(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), s(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), s(x1)) -> c3(A__ADD(a__p(mark(z0)), s(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), s(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), s(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), s(x1)) -> c3(A__ADD(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__ADD(s(0), s(x1)) -> c3(A__ADD(0, s(mark(x1)))) A__ADD(s(fact(z0)), 0) -> c3(A__ADD(a__fact(mark(z0)), 0), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), 0) -> c3(A__ADD(a__if(mark(z0), z1, z2), 0), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), 0) -> c3(A__ADD(a__zero(mark(z0)), 0), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), 0) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), 0), MARK(prod(z0, z1))) A__ADD(s(p(z0)), 0) -> c3(A__ADD(a__p(mark(z0)), 0), MARK(p(z0))) A__ADD(s(add(z0, z1)), 0) -> c3(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) A__ADD(s(s(z0)), 0) -> c3(A__ADD(s(mark(z0)), 0), MARK(s(z0))) A__ADD(s(0), 0) -> c3(A__ADD(0, 0)) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__PROD_2, A__FACT_1 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c27_1, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1, c24_2, c25_2, c25_1, c26_2, c26_1, c_2, c_1 ---------------------------------------- (173) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__ADD(s(x0), true) -> c3(A__ADD(mark(x0), true), MARK(x0)) by A__ADD(s(fact(z0)), true) -> c3(A__ADD(a__fact(mark(z0)), true), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), true) -> c3(A__ADD(a__if(mark(z0), z1, z2), true), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), true) -> c3(A__ADD(a__zero(mark(z0)), true), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), true) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), true), MARK(prod(z0, z1))) A__ADD(s(p(z0)), true) -> c3(A__ADD(a__p(mark(z0)), true), MARK(p(z0))) A__ADD(s(add(z0, z1)), true) -> c3(A__ADD(a__add(mark(z0), mark(z1)), true), MARK(add(z0, z1))) A__ADD(s(s(z0)), true) -> c3(A__ADD(s(mark(z0)), true), MARK(s(z0))) A__ADD(s(0), true) -> c3(A__ADD(0, true), MARK(0)) A__ADD(s(true), true) -> c3(A__ADD(true, true), MARK(true)) A__ADD(s(false), true) -> c3(A__ADD(false, true), MARK(false)) ---------------------------------------- (174) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), 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false)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(x0)) A__ADD(s(x0), prod(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(p(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(0, x2)) -> c3(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(true, x2)) -> c3(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(false, x2)) -> c3(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), prod(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2)))) A__ADD(s(x0), p(x1)) -> c3(A__ADD(mark(x0), p(mark(x1))), MARK(x0)) A__ADD(s(x0), p(fact(z0))) -> c3(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), p(zero(z0))) -> c3(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(p(z0))) -> c3(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(add(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(s(z0))) -> c3(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(0)) -> c3(A__ADD(mark(x0), a__p(0)), MARK(x0)) A__ADD(s(x0), p(true)) -> c3(A__ADD(mark(x0), a__p(true)), MARK(x0)) A__ADD(s(x0), p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1)))) A__ADD(s(x0), add(x1, x2)) -> c3(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), add(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), add(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, p(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, s(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, 0)) -> c3(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), add(x1, true)) -> c3(A__ADD(mark(x0), a__add(mark(x1), true)), MARK(x0)) A__ADD(s(x0), add(x1, false)) -> c3(A__ADD(mark(x0), a__add(mark(x1), false)), MARK(x0)) A__ADD(s(x0), add(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), add(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(p(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(s(z0), x2)) -> c3(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(0, x2)) -> c3(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) A__ADD(s(x0), add(true, x2)) -> c3(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(x0)) A__ADD(s(x0), add(false, x2)) -> c3(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), add(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), add(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), add(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__add(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), add(x1, x2)) -> c3(A__ADD(0, a__add(mark(x1), mark(x2)))) A__ADD(s(x0), s(fact(z0))) -> c3(A__ADD(mark(x0), s(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), s(zero(z0))) -> c3(A__ADD(mark(x0), s(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(prod(z0, z1))) -> c3(A__ADD(mark(x0), s(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(p(z0))) -> c3(A__ADD(mark(x0), s(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(add(z0, z1))) -> c3(A__ADD(mark(x0), s(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(s(z0))) -> c3(A__ADD(mark(x0), s(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(0)) -> c3(A__ADD(mark(x0), s(0)), MARK(x0)) A__ADD(s(x0), s(true)) -> c3(A__ADD(mark(x0), s(true)), MARK(x0)) A__ADD(s(x0), s(false)) -> c3(A__ADD(mark(x0), s(false)), MARK(x0)) A__ADD(s(fact(z0)), s(x1)) -> c3(A__ADD(a__fact(mark(z0)), s(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), s(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), s(x1)) -> c3(A__ADD(a__zero(mark(z0)), s(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), s(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), s(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), s(x1)) -> c3(A__ADD(a__p(mark(z0)), s(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), s(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), s(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), s(x1)) -> c3(A__ADD(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__ADD(s(0), s(x1)) -> c3(A__ADD(0, s(mark(x1)))) A__ADD(s(fact(z0)), 0) -> c3(A__ADD(a__fact(mark(z0)), 0), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), 0) -> c3(A__ADD(a__if(mark(z0), z1, z2), 0), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), 0) -> c3(A__ADD(a__zero(mark(z0)), 0), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), 0) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), 0), MARK(prod(z0, z1))) A__ADD(s(p(z0)), 0) -> c3(A__ADD(a__p(mark(z0)), 0), MARK(p(z0))) A__ADD(s(add(z0, z1)), 0) -> c3(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) A__ADD(s(s(z0)), 0) -> c3(A__ADD(s(mark(z0)), 0), MARK(s(z0))) A__ADD(s(0), 0) -> c3(A__ADD(0, 0)) A__ADD(s(fact(z0)), true) -> c3(A__ADD(a__fact(mark(z0)), true), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), true) -> c3(A__ADD(a__if(mark(z0), z1, z2), true), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), true) -> c3(A__ADD(a__zero(mark(z0)), true), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), true) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), true), MARK(prod(z0, z1))) A__ADD(s(p(z0)), true) -> c3(A__ADD(a__p(mark(z0)), true), MARK(p(z0))) A__ADD(s(add(z0, z1)), true) -> c3(A__ADD(a__add(mark(z0), mark(z1)), true), MARK(add(z0, z1))) A__ADD(s(s(z0)), true) -> c3(A__ADD(s(mark(z0)), true), MARK(s(z0))) A__ADD(s(0), true) -> c3(A__ADD(0, true), MARK(0)) A__ADD(s(true), true) -> c3(A__ADD(true, true), MARK(true)) A__ADD(s(false), true) -> c3(A__ADD(false, true), MARK(false)) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1)))) A__ADD(s(x0), prod(x1, x2)) -> c3(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), prod(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, p(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, s(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, 0)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), prod(x1, true)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(x0)) A__ADD(s(x0), prod(x1, false)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(x0)) A__ADD(s(x0), prod(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(p(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(0, x2)) -> c3(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(true, x2)) -> c3(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(false, x2)) -> c3(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), prod(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2)))) A__ADD(s(x0), p(x1)) -> c3(A__ADD(mark(x0), p(mark(x1))), MARK(x0)) A__ADD(s(x0), p(fact(z0))) -> c3(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), p(zero(z0))) -> c3(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(p(z0))) -> c3(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(add(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(s(z0))) -> c3(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(0)) -> c3(A__ADD(mark(x0), a__p(0)), MARK(x0)) A__ADD(s(x0), p(true)) -> c3(A__ADD(mark(x0), a__p(true)), MARK(x0)) A__ADD(s(x0), p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1)))) A__ADD(s(x0), add(x1, x2)) -> c3(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), add(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), add(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, p(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, s(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, 0)) -> c3(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), add(x1, true)) -> c3(A__ADD(mark(x0), a__add(mark(x1), true)), MARK(x0)) A__ADD(s(x0), add(x1, false)) -> c3(A__ADD(mark(x0), a__add(mark(x1), false)), MARK(x0)) A__ADD(s(x0), add(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), add(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(p(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(s(z0), x2)) -> c3(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(0, x2)) -> c3(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) A__ADD(s(x0), add(true, x2)) -> c3(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(x0)) A__ADD(s(x0), add(false, x2)) -> c3(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), add(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), add(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), add(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__add(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), add(x1, x2)) -> c3(A__ADD(0, a__add(mark(x1), mark(x2)))) A__ADD(s(x0), s(fact(z0))) -> c3(A__ADD(mark(x0), s(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), s(zero(z0))) -> c3(A__ADD(mark(x0), s(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(prod(z0, z1))) -> c3(A__ADD(mark(x0), s(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(p(z0))) -> c3(A__ADD(mark(x0), s(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(add(z0, z1))) -> c3(A__ADD(mark(x0), s(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(s(z0))) -> c3(A__ADD(mark(x0), s(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(0)) -> c3(A__ADD(mark(x0), s(0)), MARK(x0)) A__ADD(s(x0), s(true)) -> c3(A__ADD(mark(x0), s(true)), MARK(x0)) A__ADD(s(x0), s(false)) -> c3(A__ADD(mark(x0), s(false)), MARK(x0)) A__ADD(s(fact(z0)), s(x1)) -> c3(A__ADD(a__fact(mark(z0)), s(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), s(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), s(x1)) -> c3(A__ADD(a__zero(mark(z0)), s(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), s(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), s(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), s(x1)) -> c3(A__ADD(a__p(mark(z0)), s(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), s(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), s(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), s(x1)) -> c3(A__ADD(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__ADD(s(0), s(x1)) -> c3(A__ADD(0, s(mark(x1)))) A__ADD(s(fact(z0)), 0) -> c3(A__ADD(a__fact(mark(z0)), 0), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), 0) -> c3(A__ADD(a__if(mark(z0), z1, z2), 0), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), 0) -> c3(A__ADD(a__zero(mark(z0)), 0), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), 0) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), 0), MARK(prod(z0, z1))) A__ADD(s(p(z0)), 0) -> c3(A__ADD(a__p(mark(z0)), 0), MARK(p(z0))) A__ADD(s(add(z0, z1)), 0) -> c3(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) A__ADD(s(s(z0)), 0) -> c3(A__ADD(s(mark(z0)), 0), MARK(s(z0))) A__ADD(s(0), 0) -> c3(A__ADD(0, 0)) A__ADD(s(fact(z0)), true) -> c3(A__ADD(a__fact(mark(z0)), true), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), true) -> c3(A__ADD(a__if(mark(z0), z1, z2), true), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), true) -> c3(A__ADD(a__zero(mark(z0)), true), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), true) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), true), MARK(prod(z0, z1))) A__ADD(s(p(z0)), true) -> c3(A__ADD(a__p(mark(z0)), true), MARK(p(z0))) A__ADD(s(add(z0, z1)), true) -> c3(A__ADD(a__add(mark(z0), mark(z1)), true), MARK(add(z0, z1))) A__ADD(s(s(z0)), true) -> c3(A__ADD(s(mark(z0)), true), MARK(s(z0))) A__ADD(s(0), true) -> c3(A__ADD(0, true), MARK(0)) A__ADD(s(true), true) -> c3(A__ADD(true, true), MARK(true)) A__ADD(s(false), true) -> c3(A__ADD(false, true), MARK(false)) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__PROD_2, A__FACT_1 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c27_1, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1, c24_2, c25_2, c25_1, c26_2, c26_1, c_2, c_1 ---------------------------------------- (175) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: A__ADD(s(false), true) -> c3(A__ADD(false, true), MARK(false)) A__ADD(s(true), true) -> c3(A__ADD(true, true), MARK(true)) ---------------------------------------- (176) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> 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a__prod(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), prod(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, p(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, s(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, 0)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), prod(x1, true)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(x0)) A__ADD(s(x0), prod(x1, false)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(x0)) A__ADD(s(x0), prod(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(p(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(0, x2)) -> c3(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(true, x2)) -> c3(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(false, x2)) -> c3(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), prod(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2)))) A__ADD(s(x0), p(x1)) -> c3(A__ADD(mark(x0), p(mark(x1))), MARK(x0)) A__ADD(s(x0), p(fact(z0))) -> c3(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), p(zero(z0))) -> c3(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(p(z0))) -> c3(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(add(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(s(z0))) -> c3(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(0)) -> c3(A__ADD(mark(x0), a__p(0)), MARK(x0)) A__ADD(s(x0), p(true)) -> c3(A__ADD(mark(x0), a__p(true)), MARK(x0)) A__ADD(s(x0), p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1)))) A__ADD(s(x0), add(x1, x2)) -> c3(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), add(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), add(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, p(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, s(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, 0)) -> c3(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), add(x1, true)) -> c3(A__ADD(mark(x0), a__add(mark(x1), true)), MARK(x0)) A__ADD(s(x0), add(x1, false)) -> c3(A__ADD(mark(x0), a__add(mark(x1), false)), MARK(x0)) A__ADD(s(x0), add(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), add(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(p(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(s(z0), x2)) -> c3(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(0, x2)) -> c3(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) A__ADD(s(x0), add(true, x2)) -> c3(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(x0)) A__ADD(s(x0), add(false, x2)) -> c3(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), add(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), add(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), add(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__add(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), add(x1, x2)) -> c3(A__ADD(0, a__add(mark(x1), mark(x2)))) A__ADD(s(x0), s(fact(z0))) -> c3(A__ADD(mark(x0), s(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), s(zero(z0))) -> c3(A__ADD(mark(x0), s(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(prod(z0, z1))) -> c3(A__ADD(mark(x0), s(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(p(z0))) -> c3(A__ADD(mark(x0), s(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(add(z0, z1))) -> c3(A__ADD(mark(x0), s(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(s(z0))) -> c3(A__ADD(mark(x0), s(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(0)) -> c3(A__ADD(mark(x0), s(0)), MARK(x0)) A__ADD(s(x0), s(true)) -> c3(A__ADD(mark(x0), s(true)), MARK(x0)) A__ADD(s(x0), s(false)) -> c3(A__ADD(mark(x0), s(false)), MARK(x0)) A__ADD(s(fact(z0)), s(x1)) -> c3(A__ADD(a__fact(mark(z0)), s(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), s(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), s(x1)) -> c3(A__ADD(a__zero(mark(z0)), s(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), s(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), s(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), s(x1)) -> c3(A__ADD(a__p(mark(z0)), s(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), s(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), s(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), s(x1)) -> c3(A__ADD(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__ADD(s(0), s(x1)) -> c3(A__ADD(0, s(mark(x1)))) A__ADD(s(fact(z0)), 0) -> c3(A__ADD(a__fact(mark(z0)), 0), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), 0) -> c3(A__ADD(a__if(mark(z0), z1, z2), 0), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), 0) -> c3(A__ADD(a__zero(mark(z0)), 0), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), 0) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), 0), MARK(prod(z0, z1))) A__ADD(s(p(z0)), 0) -> c3(A__ADD(a__p(mark(z0)), 0), MARK(p(z0))) A__ADD(s(add(z0, z1)), 0) -> c3(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) A__ADD(s(s(z0)), 0) -> c3(A__ADD(s(mark(z0)), 0), MARK(s(z0))) A__ADD(s(0), 0) -> c3(A__ADD(0, 0)) A__ADD(s(fact(z0)), true) -> c3(A__ADD(a__fact(mark(z0)), true), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), true) -> c3(A__ADD(a__if(mark(z0), z1, z2), true), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), true) -> c3(A__ADD(a__zero(mark(z0)), true), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), true) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), true), MARK(prod(z0, z1))) A__ADD(s(p(z0)), true) -> c3(A__ADD(a__p(mark(z0)), true), MARK(p(z0))) A__ADD(s(add(z0, z1)), true) -> c3(A__ADD(a__add(mark(z0), mark(z1)), true), MARK(add(z0, z1))) A__ADD(s(s(z0)), true) -> c3(A__ADD(s(mark(z0)), true), MARK(s(z0))) A__ADD(s(0), true) -> c3(A__ADD(0, true), MARK(0)) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> 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A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1)))) A__ADD(s(x0), prod(x1, x2)) -> c3(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), prod(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, p(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, s(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, 0)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), prod(x1, true)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(x0)) A__ADD(s(x0), prod(x1, false)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(x0)) A__ADD(s(x0), prod(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(p(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(0, x2)) -> c3(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(true, x2)) -> c3(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(false, x2)) -> c3(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), prod(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2)))) A__ADD(s(x0), p(x1)) -> c3(A__ADD(mark(x0), p(mark(x1))), MARK(x0)) A__ADD(s(x0), p(fact(z0))) -> c3(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), p(zero(z0))) -> c3(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(p(z0))) -> c3(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(add(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(s(z0))) -> c3(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(0)) -> c3(A__ADD(mark(x0), a__p(0)), MARK(x0)) A__ADD(s(x0), p(true)) -> c3(A__ADD(mark(x0), a__p(true)), MARK(x0)) A__ADD(s(x0), p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1)))) A__ADD(s(x0), add(x1, x2)) -> c3(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), add(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), add(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, p(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, s(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, 0)) -> c3(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), add(x1, true)) -> c3(A__ADD(mark(x0), a__add(mark(x1), true)), MARK(x0)) A__ADD(s(x0), add(x1, false)) -> c3(A__ADD(mark(x0), a__add(mark(x1), false)), MARK(x0)) A__ADD(s(x0), add(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), add(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(p(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(s(z0), x2)) -> c3(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(0, x2)) -> c3(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) A__ADD(s(x0), add(true, x2)) -> c3(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(x0)) A__ADD(s(x0), add(false, x2)) -> c3(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), add(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), add(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), add(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__add(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), add(x1, x2)) -> c3(A__ADD(0, a__add(mark(x1), mark(x2)))) A__ADD(s(x0), s(fact(z0))) -> c3(A__ADD(mark(x0), s(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), s(zero(z0))) -> c3(A__ADD(mark(x0), s(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(prod(z0, z1))) -> c3(A__ADD(mark(x0), s(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(p(z0))) -> c3(A__ADD(mark(x0), s(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(add(z0, z1))) -> c3(A__ADD(mark(x0), s(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(s(z0))) -> c3(A__ADD(mark(x0), s(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(0)) -> c3(A__ADD(mark(x0), s(0)), MARK(x0)) A__ADD(s(x0), s(true)) -> c3(A__ADD(mark(x0), s(true)), MARK(x0)) A__ADD(s(x0), s(false)) -> c3(A__ADD(mark(x0), s(false)), MARK(x0)) A__ADD(s(fact(z0)), s(x1)) -> c3(A__ADD(a__fact(mark(z0)), s(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), s(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), s(x1)) -> c3(A__ADD(a__zero(mark(z0)), s(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), s(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), s(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), s(x1)) -> c3(A__ADD(a__p(mark(z0)), s(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), s(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), s(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), s(x1)) -> c3(A__ADD(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__ADD(s(0), s(x1)) -> c3(A__ADD(0, s(mark(x1)))) A__ADD(s(fact(z0)), 0) -> c3(A__ADD(a__fact(mark(z0)), 0), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), 0) -> c3(A__ADD(a__if(mark(z0), z1, z2), 0), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), 0) -> c3(A__ADD(a__zero(mark(z0)), 0), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), 0) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), 0), MARK(prod(z0, z1))) A__ADD(s(p(z0)), 0) -> c3(A__ADD(a__p(mark(z0)), 0), MARK(p(z0))) A__ADD(s(add(z0, z1)), 0) -> c3(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) A__ADD(s(s(z0)), 0) -> c3(A__ADD(s(mark(z0)), 0), MARK(s(z0))) A__ADD(s(0), 0) -> c3(A__ADD(0, 0)) A__ADD(s(fact(z0)), true) -> c3(A__ADD(a__fact(mark(z0)), true), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), true) -> c3(A__ADD(a__if(mark(z0), z1, z2), true), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), true) -> c3(A__ADD(a__zero(mark(z0)), true), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), true) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), true), MARK(prod(z0, z1))) A__ADD(s(p(z0)), true) -> c3(A__ADD(a__p(mark(z0)), true), MARK(p(z0))) A__ADD(s(add(z0, z1)), true) -> c3(A__ADD(a__add(mark(z0), mark(z1)), true), MARK(add(z0, z1))) A__ADD(s(s(z0)), true) -> c3(A__ADD(s(mark(z0)), true), MARK(s(z0))) A__ADD(s(0), true) -> c3(A__ADD(0, true), MARK(0)) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__PROD_2, A__FACT_1 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c27_1, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1, c24_2, c25_2, c25_1, c26_2, c26_1, c_2, c_1 ---------------------------------------- (177) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (178) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1)))) A__ADD(s(x0), prod(x1, x2)) -> c3(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), prod(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, p(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, s(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, 0)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), prod(x1, true)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(x0)) A__ADD(s(x0), prod(x1, false)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(x0)) A__ADD(s(x0), prod(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(p(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(0, x2)) -> c3(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(true, x2)) -> c3(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(false, x2)) -> c3(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), prod(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2)))) A__ADD(s(x0), p(x1)) -> c3(A__ADD(mark(x0), p(mark(x1))), MARK(x0)) A__ADD(s(x0), p(fact(z0))) -> c3(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), p(zero(z0))) -> c3(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(p(z0))) -> c3(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(add(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(s(z0))) -> c3(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(0)) -> c3(A__ADD(mark(x0), a__p(0)), MARK(x0)) A__ADD(s(x0), p(true)) -> c3(A__ADD(mark(x0), a__p(true)), MARK(x0)) A__ADD(s(x0), p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1)))) A__ADD(s(x0), add(x1, x2)) -> c3(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), add(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), add(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, p(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, s(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, 0)) -> c3(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), add(x1, true)) -> c3(A__ADD(mark(x0), a__add(mark(x1), true)), MARK(x0)) A__ADD(s(x0), add(x1, false)) -> c3(A__ADD(mark(x0), a__add(mark(x1), false)), MARK(x0)) A__ADD(s(x0), add(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), add(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(p(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(s(z0), x2)) -> c3(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(0, x2)) -> c3(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) A__ADD(s(x0), add(true, x2)) -> c3(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(x0)) A__ADD(s(x0), add(false, x2)) -> c3(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), add(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), add(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), add(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__add(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), add(x1, x2)) -> c3(A__ADD(0, a__add(mark(x1), mark(x2)))) A__ADD(s(x0), s(fact(z0))) -> c3(A__ADD(mark(x0), s(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), s(zero(z0))) -> c3(A__ADD(mark(x0), s(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(prod(z0, z1))) -> c3(A__ADD(mark(x0), s(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(p(z0))) -> c3(A__ADD(mark(x0), s(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(add(z0, z1))) -> c3(A__ADD(mark(x0), s(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(s(z0))) -> c3(A__ADD(mark(x0), s(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(0)) -> c3(A__ADD(mark(x0), s(0)), MARK(x0)) A__ADD(s(x0), s(true)) -> c3(A__ADD(mark(x0), s(true)), MARK(x0)) A__ADD(s(x0), s(false)) -> c3(A__ADD(mark(x0), s(false)), MARK(x0)) A__ADD(s(fact(z0)), s(x1)) -> c3(A__ADD(a__fact(mark(z0)), s(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), s(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), s(x1)) -> c3(A__ADD(a__zero(mark(z0)), s(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), s(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), s(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), s(x1)) -> c3(A__ADD(a__p(mark(z0)), s(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), s(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), s(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), s(x1)) -> c3(A__ADD(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__ADD(s(0), s(x1)) -> c3(A__ADD(0, s(mark(x1)))) A__ADD(s(fact(z0)), 0) -> c3(A__ADD(a__fact(mark(z0)), 0), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), 0) -> c3(A__ADD(a__if(mark(z0), z1, z2), 0), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), 0) -> c3(A__ADD(a__zero(mark(z0)), 0), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), 0) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), 0), MARK(prod(z0, z1))) A__ADD(s(p(z0)), 0) -> c3(A__ADD(a__p(mark(z0)), 0), MARK(p(z0))) A__ADD(s(add(z0, z1)), 0) -> c3(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) A__ADD(s(s(z0)), 0) -> c3(A__ADD(s(mark(z0)), 0), MARK(s(z0))) A__ADD(s(0), 0) -> c3(A__ADD(0, 0)) A__ADD(s(fact(z0)), true) -> c3(A__ADD(a__fact(mark(z0)), true), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), true) -> c3(A__ADD(a__if(mark(z0), z1, z2), true), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), true) -> c3(A__ADD(a__zero(mark(z0)), true), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), true) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), true), MARK(prod(z0, z1))) A__ADD(s(p(z0)), true) -> c3(A__ADD(a__p(mark(z0)), true), MARK(p(z0))) A__ADD(s(add(z0, z1)), true) -> c3(A__ADD(a__add(mark(z0), mark(z1)), true), MARK(add(z0, z1))) A__ADD(s(s(z0)), true) -> c3(A__ADD(s(mark(z0)), true), MARK(s(z0))) A__ADD(s(0), true) -> c3(A__ADD(0, true)) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1)))) A__ADD(s(x0), prod(x1, x2)) -> c3(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), prod(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, p(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, s(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, 0)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), prod(x1, true)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(x0)) A__ADD(s(x0), prod(x1, false)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(x0)) A__ADD(s(x0), prod(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(p(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(0, x2)) -> c3(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(true, x2)) -> c3(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(false, x2)) -> c3(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), prod(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2)))) A__ADD(s(x0), p(x1)) -> c3(A__ADD(mark(x0), p(mark(x1))), MARK(x0)) A__ADD(s(x0), p(fact(z0))) -> c3(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), p(zero(z0))) -> c3(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(p(z0))) -> c3(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(add(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(s(z0))) -> c3(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(0)) -> c3(A__ADD(mark(x0), a__p(0)), MARK(x0)) A__ADD(s(x0), p(true)) -> c3(A__ADD(mark(x0), a__p(true)), MARK(x0)) A__ADD(s(x0), p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1)))) A__ADD(s(x0), add(x1, x2)) -> c3(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), add(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), add(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, p(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, s(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, 0)) -> c3(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), add(x1, true)) -> c3(A__ADD(mark(x0), a__add(mark(x1), true)), MARK(x0)) A__ADD(s(x0), add(x1, false)) -> c3(A__ADD(mark(x0), a__add(mark(x1), false)), MARK(x0)) A__ADD(s(x0), add(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), add(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(p(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(s(z0), x2)) -> c3(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(0, x2)) -> c3(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) A__ADD(s(x0), add(true, x2)) -> c3(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(x0)) A__ADD(s(x0), add(false, x2)) -> c3(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), add(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), add(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), add(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__add(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), add(x1, x2)) -> c3(A__ADD(0, a__add(mark(x1), mark(x2)))) A__ADD(s(x0), s(fact(z0))) -> c3(A__ADD(mark(x0), s(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), s(zero(z0))) -> c3(A__ADD(mark(x0), s(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(prod(z0, z1))) -> c3(A__ADD(mark(x0), s(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(p(z0))) -> c3(A__ADD(mark(x0), s(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(add(z0, z1))) -> c3(A__ADD(mark(x0), s(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(s(z0))) -> c3(A__ADD(mark(x0), s(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(0)) -> c3(A__ADD(mark(x0), s(0)), MARK(x0)) A__ADD(s(x0), s(true)) -> c3(A__ADD(mark(x0), s(true)), MARK(x0)) A__ADD(s(x0), s(false)) -> c3(A__ADD(mark(x0), s(false)), MARK(x0)) A__ADD(s(fact(z0)), s(x1)) -> c3(A__ADD(a__fact(mark(z0)), s(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), s(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), s(x1)) -> c3(A__ADD(a__zero(mark(z0)), s(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), s(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), s(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), s(x1)) -> c3(A__ADD(a__p(mark(z0)), s(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), s(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), s(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), s(x1)) -> c3(A__ADD(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__ADD(s(0), s(x1)) -> c3(A__ADD(0, s(mark(x1)))) A__ADD(s(fact(z0)), 0) -> c3(A__ADD(a__fact(mark(z0)), 0), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), 0) -> c3(A__ADD(a__if(mark(z0), z1, z2), 0), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), 0) -> c3(A__ADD(a__zero(mark(z0)), 0), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), 0) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), 0), MARK(prod(z0, z1))) A__ADD(s(p(z0)), 0) -> c3(A__ADD(a__p(mark(z0)), 0), MARK(p(z0))) A__ADD(s(add(z0, z1)), 0) -> c3(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) A__ADD(s(s(z0)), 0) -> c3(A__ADD(s(mark(z0)), 0), MARK(s(z0))) A__ADD(s(0), 0) -> c3(A__ADD(0, 0)) A__ADD(s(fact(z0)), true) -> c3(A__ADD(a__fact(mark(z0)), true), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), true) -> c3(A__ADD(a__if(mark(z0), z1, z2), true), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), true) -> c3(A__ADD(a__zero(mark(z0)), true), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), true) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), true), MARK(prod(z0, z1))) A__ADD(s(p(z0)), true) -> c3(A__ADD(a__p(mark(z0)), true), MARK(p(z0))) A__ADD(s(add(z0, z1)), true) -> c3(A__ADD(a__add(mark(z0), mark(z1)), true), MARK(add(z0, z1))) A__ADD(s(s(z0)), true) -> c3(A__ADD(s(mark(z0)), true), MARK(s(z0))) A__ADD(s(0), true) -> c3(A__ADD(0, true)) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__PROD_2, A__FACT_1 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c27_1, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1, c24_2, c25_2, c25_1, c26_2, c26_1, c_2, c_1 ---------------------------------------- (179) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__ADD(s(x0), false) -> c3(A__ADD(mark(x0), false), MARK(x0)) by A__ADD(s(fact(z0)), false) -> c3(A__ADD(a__fact(mark(z0)), false), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), false) -> c3(A__ADD(a__if(mark(z0), z1, z2), false), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), false) -> c3(A__ADD(a__zero(mark(z0)), false), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), false) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), false), MARK(prod(z0, z1))) A__ADD(s(p(z0)), false) -> c3(A__ADD(a__p(mark(z0)), false), MARK(p(z0))) A__ADD(s(add(z0, z1)), false) -> c3(A__ADD(a__add(mark(z0), mark(z1)), false), MARK(add(z0, z1))) A__ADD(s(s(z0)), false) -> c3(A__ADD(s(mark(z0)), false), MARK(s(z0))) A__ADD(s(0), false) -> c3(A__ADD(0, false), MARK(0)) A__ADD(s(true), false) -> c3(A__ADD(true, false), MARK(true)) A__ADD(s(false), false) -> c3(A__ADD(false, false), MARK(false)) ---------------------------------------- (180) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1)))) A__ADD(s(x0), prod(x1, x2)) -> c3(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), prod(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, p(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, s(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, 0)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), prod(x1, true)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(x0)) A__ADD(s(x0), prod(x1, false)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(x0)) A__ADD(s(x0), prod(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(p(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(0, x2)) -> c3(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(true, x2)) -> c3(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(false, x2)) -> c3(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), prod(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2)))) A__ADD(s(x0), p(x1)) -> c3(A__ADD(mark(x0), p(mark(x1))), MARK(x0)) A__ADD(s(x0), p(fact(z0))) -> c3(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), p(zero(z0))) -> c3(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(p(z0))) -> c3(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(add(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(s(z0))) -> c3(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(0)) -> c3(A__ADD(mark(x0), a__p(0)), MARK(x0)) A__ADD(s(x0), p(true)) -> c3(A__ADD(mark(x0), a__p(true)), MARK(x0)) A__ADD(s(x0), p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1)))) A__ADD(s(x0), add(x1, x2)) -> c3(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), add(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), add(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, p(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, s(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, 0)) -> c3(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), add(x1, true)) -> c3(A__ADD(mark(x0), a__add(mark(x1), true)), MARK(x0)) A__ADD(s(x0), add(x1, false)) -> c3(A__ADD(mark(x0), a__add(mark(x1), false)), MARK(x0)) A__ADD(s(x0), add(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), add(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(p(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(s(z0), x2)) -> c3(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(0, x2)) -> c3(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) A__ADD(s(x0), add(true, x2)) -> c3(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(x0)) A__ADD(s(x0), add(false, x2)) -> c3(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), add(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), add(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), add(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__add(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), add(x1, x2)) -> c3(A__ADD(0, a__add(mark(x1), mark(x2)))) A__ADD(s(x0), s(fact(z0))) -> c3(A__ADD(mark(x0), s(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), s(zero(z0))) -> c3(A__ADD(mark(x0), s(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(prod(z0, z1))) -> c3(A__ADD(mark(x0), s(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(p(z0))) -> c3(A__ADD(mark(x0), s(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(add(z0, z1))) -> c3(A__ADD(mark(x0), s(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(s(z0))) -> c3(A__ADD(mark(x0), s(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(0)) -> c3(A__ADD(mark(x0), s(0)), MARK(x0)) A__ADD(s(x0), s(true)) -> c3(A__ADD(mark(x0), s(true)), MARK(x0)) A__ADD(s(x0), s(false)) -> c3(A__ADD(mark(x0), s(false)), MARK(x0)) A__ADD(s(fact(z0)), s(x1)) -> c3(A__ADD(a__fact(mark(z0)), s(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), s(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), s(x1)) -> c3(A__ADD(a__zero(mark(z0)), s(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), s(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), s(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), s(x1)) -> c3(A__ADD(a__p(mark(z0)), s(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), s(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), s(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), s(x1)) -> c3(A__ADD(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__ADD(s(0), s(x1)) -> c3(A__ADD(0, s(mark(x1)))) A__ADD(s(fact(z0)), 0) -> c3(A__ADD(a__fact(mark(z0)), 0), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), 0) -> c3(A__ADD(a__if(mark(z0), z1, z2), 0), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), 0) -> c3(A__ADD(a__zero(mark(z0)), 0), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), 0) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), 0), MARK(prod(z0, z1))) A__ADD(s(p(z0)), 0) -> c3(A__ADD(a__p(mark(z0)), 0), MARK(p(z0))) A__ADD(s(add(z0, z1)), 0) -> c3(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) A__ADD(s(s(z0)), 0) -> c3(A__ADD(s(mark(z0)), 0), MARK(s(z0))) A__ADD(s(0), 0) -> c3(A__ADD(0, 0)) A__ADD(s(fact(z0)), true) -> c3(A__ADD(a__fact(mark(z0)), true), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), true) -> c3(A__ADD(a__if(mark(z0), z1, z2), true), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), true) -> c3(A__ADD(a__zero(mark(z0)), true), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), true) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), true), MARK(prod(z0, z1))) A__ADD(s(p(z0)), true) -> c3(A__ADD(a__p(mark(z0)), true), MARK(p(z0))) A__ADD(s(add(z0, z1)), true) -> c3(A__ADD(a__add(mark(z0), mark(z1)), true), MARK(add(z0, z1))) A__ADD(s(s(z0)), true) -> c3(A__ADD(s(mark(z0)), true), MARK(s(z0))) A__ADD(s(0), true) -> c3(A__ADD(0, true)) A__ADD(s(fact(z0)), false) -> c3(A__ADD(a__fact(mark(z0)), false), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), false) -> c3(A__ADD(a__if(mark(z0), z1, z2), false), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), false) -> c3(A__ADD(a__zero(mark(z0)), false), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), false) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), false), MARK(prod(z0, z1))) A__ADD(s(p(z0)), false) -> c3(A__ADD(a__p(mark(z0)), false), MARK(p(z0))) A__ADD(s(add(z0, z1)), false) -> c3(A__ADD(a__add(mark(z0), mark(z1)), false), MARK(add(z0, z1))) A__ADD(s(s(z0)), false) -> c3(A__ADD(s(mark(z0)), false), MARK(s(z0))) A__ADD(s(0), false) -> c3(A__ADD(0, false), MARK(0)) A__ADD(s(true), false) -> c3(A__ADD(true, false), MARK(true)) A__ADD(s(false), false) -> c3(A__ADD(false, false), MARK(false)) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), 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MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, 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c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, 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a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1)))) A__ADD(s(x0), prod(x1, x2)) -> c3(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), prod(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, p(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, s(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, 0)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), prod(x1, true)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(x0)) A__ADD(s(x0), prod(x1, false)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(x0)) A__ADD(s(x0), prod(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(p(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(0, x2)) -> c3(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(true, x2)) -> c3(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(false, x2)) -> c3(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), prod(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2)))) A__ADD(s(x0), p(x1)) -> c3(A__ADD(mark(x0), p(mark(x1))), MARK(x0)) A__ADD(s(x0), p(fact(z0))) -> c3(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), p(zero(z0))) -> c3(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(p(z0))) -> c3(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(add(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(s(z0))) -> c3(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(0)) -> c3(A__ADD(mark(x0), a__p(0)), MARK(x0)) A__ADD(s(x0), p(true)) -> c3(A__ADD(mark(x0), a__p(true)), MARK(x0)) A__ADD(s(x0), p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1)))) A__ADD(s(x0), add(x1, x2)) -> c3(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), add(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), add(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, p(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, s(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, 0)) -> c3(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), add(x1, true)) -> c3(A__ADD(mark(x0), a__add(mark(x1), true)), MARK(x0)) A__ADD(s(x0), add(x1, false)) -> c3(A__ADD(mark(x0), a__add(mark(x1), false)), MARK(x0)) A__ADD(s(x0), add(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), add(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(p(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(s(z0), x2)) -> c3(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(0, x2)) -> c3(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) A__ADD(s(x0), add(true, x2)) -> c3(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(x0)) A__ADD(s(x0), add(false, x2)) -> c3(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), add(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), add(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), add(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__add(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), add(x1, x2)) -> c3(A__ADD(0, a__add(mark(x1), mark(x2)))) A__ADD(s(x0), s(fact(z0))) -> c3(A__ADD(mark(x0), s(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), s(zero(z0))) -> c3(A__ADD(mark(x0), s(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(prod(z0, z1))) -> c3(A__ADD(mark(x0), s(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(p(z0))) -> c3(A__ADD(mark(x0), s(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(add(z0, z1))) -> c3(A__ADD(mark(x0), s(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(s(z0))) -> c3(A__ADD(mark(x0), s(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(0)) -> c3(A__ADD(mark(x0), s(0)), MARK(x0)) A__ADD(s(x0), s(true)) -> c3(A__ADD(mark(x0), s(true)), MARK(x0)) A__ADD(s(x0), s(false)) -> c3(A__ADD(mark(x0), s(false)), MARK(x0)) A__ADD(s(fact(z0)), s(x1)) -> c3(A__ADD(a__fact(mark(z0)), s(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), s(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), s(x1)) -> c3(A__ADD(a__zero(mark(z0)), s(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), s(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), s(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), s(x1)) -> c3(A__ADD(a__p(mark(z0)), s(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), s(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), s(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), s(x1)) -> c3(A__ADD(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__ADD(s(0), s(x1)) -> c3(A__ADD(0, s(mark(x1)))) A__ADD(s(fact(z0)), 0) -> c3(A__ADD(a__fact(mark(z0)), 0), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), 0) -> c3(A__ADD(a__if(mark(z0), z1, z2), 0), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), 0) -> c3(A__ADD(a__zero(mark(z0)), 0), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), 0) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), 0), MARK(prod(z0, z1))) A__ADD(s(p(z0)), 0) -> c3(A__ADD(a__p(mark(z0)), 0), MARK(p(z0))) A__ADD(s(add(z0, z1)), 0) -> c3(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) A__ADD(s(s(z0)), 0) -> c3(A__ADD(s(mark(z0)), 0), MARK(s(z0))) A__ADD(s(0), 0) -> c3(A__ADD(0, 0)) A__ADD(s(fact(z0)), true) -> c3(A__ADD(a__fact(mark(z0)), true), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), true) -> c3(A__ADD(a__if(mark(z0), z1, z2), true), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), true) -> c3(A__ADD(a__zero(mark(z0)), true), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), true) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), true), MARK(prod(z0, z1))) A__ADD(s(p(z0)), true) -> c3(A__ADD(a__p(mark(z0)), true), MARK(p(z0))) A__ADD(s(add(z0, z1)), true) -> c3(A__ADD(a__add(mark(z0), mark(z1)), true), MARK(add(z0, z1))) A__ADD(s(s(z0)), true) -> c3(A__ADD(s(mark(z0)), true), MARK(s(z0))) A__ADD(s(0), true) -> c3(A__ADD(0, true)) A__ADD(s(fact(z0)), false) -> c3(A__ADD(a__fact(mark(z0)), false), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), false) -> c3(A__ADD(a__if(mark(z0), z1, z2), false), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), false) -> c3(A__ADD(a__zero(mark(z0)), false), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), false) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), false), MARK(prod(z0, z1))) A__ADD(s(p(z0)), false) -> c3(A__ADD(a__p(mark(z0)), false), MARK(p(z0))) A__ADD(s(add(z0, z1)), false) -> c3(A__ADD(a__add(mark(z0), mark(z1)), false), MARK(add(z0, z1))) A__ADD(s(s(z0)), false) -> c3(A__ADD(s(mark(z0)), false), MARK(s(z0))) A__ADD(s(0), false) -> c3(A__ADD(0, false), MARK(0)) A__ADD(s(true), false) -> c3(A__ADD(true, false), MARK(true)) A__ADD(s(false), false) -> c3(A__ADD(false, false), MARK(false)) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__PROD_2, A__FACT_1 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c27_1, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1, c24_2, c25_2, c25_1, c26_2, c26_1, c_2, c_1 ---------------------------------------- (181) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: A__ADD(s(true), false) -> c3(A__ADD(true, false), MARK(true)) A__ADD(s(false), false) -> c3(A__ADD(false, false), MARK(false)) ---------------------------------------- (182) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1)))) A__ADD(s(x0), prod(x1, x2)) -> c3(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), prod(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, p(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, s(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, 0)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), prod(x1, true)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(x0)) A__ADD(s(x0), prod(x1, false)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(x0)) A__ADD(s(x0), prod(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(p(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(0, x2)) -> c3(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(true, x2)) -> c3(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(false, x2)) -> c3(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), prod(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2)))) A__ADD(s(x0), p(x1)) -> c3(A__ADD(mark(x0), p(mark(x1))), MARK(x0)) A__ADD(s(x0), p(fact(z0))) -> c3(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), p(zero(z0))) -> c3(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(p(z0))) -> c3(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(add(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(s(z0))) -> c3(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(0)) -> c3(A__ADD(mark(x0), a__p(0)), MARK(x0)) A__ADD(s(x0), p(true)) -> c3(A__ADD(mark(x0), a__p(true)), MARK(x0)) A__ADD(s(x0), p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1)))) A__ADD(s(x0), add(x1, x2)) -> c3(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), add(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), add(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, p(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, s(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, 0)) -> c3(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), add(x1, true)) -> c3(A__ADD(mark(x0), a__add(mark(x1), true)), MARK(x0)) A__ADD(s(x0), add(x1, false)) -> c3(A__ADD(mark(x0), a__add(mark(x1), false)), MARK(x0)) A__ADD(s(x0), add(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), add(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(p(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(s(z0), x2)) -> c3(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(0, x2)) -> c3(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) A__ADD(s(x0), add(true, x2)) -> c3(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(x0)) A__ADD(s(x0), add(false, x2)) -> c3(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), add(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), add(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), add(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__add(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), add(x1, x2)) -> c3(A__ADD(0, a__add(mark(x1), mark(x2)))) A__ADD(s(x0), s(fact(z0))) -> c3(A__ADD(mark(x0), s(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), s(zero(z0))) -> c3(A__ADD(mark(x0), s(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(prod(z0, z1))) -> c3(A__ADD(mark(x0), s(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(p(z0))) -> c3(A__ADD(mark(x0), s(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(add(z0, z1))) -> c3(A__ADD(mark(x0), s(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(s(z0))) -> c3(A__ADD(mark(x0), s(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(0)) -> c3(A__ADD(mark(x0), s(0)), MARK(x0)) A__ADD(s(x0), s(true)) -> c3(A__ADD(mark(x0), s(true)), MARK(x0)) A__ADD(s(x0), s(false)) -> c3(A__ADD(mark(x0), s(false)), MARK(x0)) A__ADD(s(fact(z0)), s(x1)) -> c3(A__ADD(a__fact(mark(z0)), s(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), s(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), s(x1)) -> c3(A__ADD(a__zero(mark(z0)), s(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), s(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), s(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), s(x1)) -> c3(A__ADD(a__p(mark(z0)), s(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), s(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), s(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), s(x1)) -> c3(A__ADD(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__ADD(s(0), s(x1)) -> c3(A__ADD(0, s(mark(x1)))) A__ADD(s(fact(z0)), 0) -> c3(A__ADD(a__fact(mark(z0)), 0), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), 0) -> c3(A__ADD(a__if(mark(z0), z1, z2), 0), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), 0) -> c3(A__ADD(a__zero(mark(z0)), 0), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), 0) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), 0), MARK(prod(z0, z1))) A__ADD(s(p(z0)), 0) -> c3(A__ADD(a__p(mark(z0)), 0), MARK(p(z0))) A__ADD(s(add(z0, z1)), 0) -> c3(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) A__ADD(s(s(z0)), 0) -> c3(A__ADD(s(mark(z0)), 0), MARK(s(z0))) A__ADD(s(0), 0) -> c3(A__ADD(0, 0)) A__ADD(s(fact(z0)), true) -> c3(A__ADD(a__fact(mark(z0)), true), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), true) -> c3(A__ADD(a__if(mark(z0), z1, z2), true), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), true) -> c3(A__ADD(a__zero(mark(z0)), true), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), true) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), true), MARK(prod(z0, z1))) A__ADD(s(p(z0)), true) -> c3(A__ADD(a__p(mark(z0)), true), MARK(p(z0))) A__ADD(s(add(z0, z1)), true) -> c3(A__ADD(a__add(mark(z0), mark(z1)), true), MARK(add(z0, z1))) A__ADD(s(s(z0)), true) -> c3(A__ADD(s(mark(z0)), true), MARK(s(z0))) A__ADD(s(0), true) -> c3(A__ADD(0, true)) A__ADD(s(fact(z0)), false) -> c3(A__ADD(a__fact(mark(z0)), false), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), false) -> c3(A__ADD(a__if(mark(z0), z1, z2), false), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), false) -> c3(A__ADD(a__zero(mark(z0)), false), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), false) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), false), MARK(prod(z0, z1))) A__ADD(s(p(z0)), false) -> c3(A__ADD(a__p(mark(z0)), false), MARK(p(z0))) A__ADD(s(add(z0, z1)), false) -> c3(A__ADD(a__add(mark(z0), mark(z1)), false), MARK(add(z0, z1))) A__ADD(s(s(z0)), false) -> c3(A__ADD(s(mark(z0)), false), MARK(s(z0))) A__ADD(s(0), false) -> c3(A__ADD(0, false), MARK(0)) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1)))) A__ADD(s(x0), prod(x1, x2)) -> c3(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), prod(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, p(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, s(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, 0)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), prod(x1, true)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(x0)) A__ADD(s(x0), prod(x1, false)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(x0)) A__ADD(s(x0), prod(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(p(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(0, x2)) -> c3(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(true, x2)) -> c3(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(false, x2)) -> c3(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), prod(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2)))) A__ADD(s(x0), p(x1)) -> c3(A__ADD(mark(x0), p(mark(x1))), MARK(x0)) A__ADD(s(x0), p(fact(z0))) -> c3(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), p(zero(z0))) -> c3(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(p(z0))) -> c3(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(add(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(s(z0))) -> c3(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(0)) -> c3(A__ADD(mark(x0), a__p(0)), MARK(x0)) A__ADD(s(x0), p(true)) -> c3(A__ADD(mark(x0), a__p(true)), MARK(x0)) A__ADD(s(x0), p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1)))) A__ADD(s(x0), add(x1, x2)) -> c3(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), add(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), add(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, p(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, s(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, 0)) -> c3(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), add(x1, true)) -> c3(A__ADD(mark(x0), a__add(mark(x1), true)), MARK(x0)) A__ADD(s(x0), add(x1, false)) -> c3(A__ADD(mark(x0), a__add(mark(x1), false)), MARK(x0)) A__ADD(s(x0), add(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), add(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(p(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(s(z0), x2)) -> c3(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(0, x2)) -> c3(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) A__ADD(s(x0), add(true, x2)) -> c3(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(x0)) A__ADD(s(x0), add(false, x2)) -> c3(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), add(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), add(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), add(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__add(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), add(x1, x2)) -> c3(A__ADD(0, a__add(mark(x1), mark(x2)))) A__ADD(s(x0), s(fact(z0))) -> c3(A__ADD(mark(x0), s(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), s(zero(z0))) -> c3(A__ADD(mark(x0), s(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(prod(z0, z1))) -> c3(A__ADD(mark(x0), s(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(p(z0))) -> c3(A__ADD(mark(x0), s(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(add(z0, z1))) -> c3(A__ADD(mark(x0), s(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(s(z0))) -> c3(A__ADD(mark(x0), s(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(0)) -> c3(A__ADD(mark(x0), s(0)), MARK(x0)) A__ADD(s(x0), s(true)) -> c3(A__ADD(mark(x0), s(true)), MARK(x0)) A__ADD(s(x0), s(false)) -> c3(A__ADD(mark(x0), s(false)), MARK(x0)) A__ADD(s(fact(z0)), s(x1)) -> c3(A__ADD(a__fact(mark(z0)), s(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), s(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), s(x1)) -> c3(A__ADD(a__zero(mark(z0)), s(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), s(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), s(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), s(x1)) -> c3(A__ADD(a__p(mark(z0)), s(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), s(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), s(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), s(x1)) -> c3(A__ADD(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__ADD(s(0), s(x1)) -> c3(A__ADD(0, s(mark(x1)))) A__ADD(s(fact(z0)), 0) -> c3(A__ADD(a__fact(mark(z0)), 0), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), 0) -> c3(A__ADD(a__if(mark(z0), z1, z2), 0), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), 0) -> c3(A__ADD(a__zero(mark(z0)), 0), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), 0) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), 0), MARK(prod(z0, z1))) A__ADD(s(p(z0)), 0) -> c3(A__ADD(a__p(mark(z0)), 0), MARK(p(z0))) A__ADD(s(add(z0, z1)), 0) -> c3(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) A__ADD(s(s(z0)), 0) -> c3(A__ADD(s(mark(z0)), 0), MARK(s(z0))) A__ADD(s(0), 0) -> c3(A__ADD(0, 0)) A__ADD(s(fact(z0)), true) -> c3(A__ADD(a__fact(mark(z0)), true), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), true) -> c3(A__ADD(a__if(mark(z0), z1, z2), true), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), true) -> c3(A__ADD(a__zero(mark(z0)), true), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), true) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), true), MARK(prod(z0, z1))) A__ADD(s(p(z0)), true) -> c3(A__ADD(a__p(mark(z0)), true), MARK(p(z0))) A__ADD(s(add(z0, z1)), true) -> c3(A__ADD(a__add(mark(z0), mark(z1)), true), MARK(add(z0, z1))) A__ADD(s(s(z0)), true) -> c3(A__ADD(s(mark(z0)), true), MARK(s(z0))) A__ADD(s(0), true) -> c3(A__ADD(0, true)) A__ADD(s(fact(z0)), false) -> c3(A__ADD(a__fact(mark(z0)), false), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), false) -> c3(A__ADD(a__if(mark(z0), z1, z2), false), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), false) -> c3(A__ADD(a__zero(mark(z0)), false), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), false) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), false), MARK(prod(z0, z1))) A__ADD(s(p(z0)), false) -> c3(A__ADD(a__p(mark(z0)), false), MARK(p(z0))) A__ADD(s(add(z0, z1)), false) -> c3(A__ADD(a__add(mark(z0), mark(z1)), false), MARK(add(z0, z1))) A__ADD(s(s(z0)), false) -> c3(A__ADD(s(mark(z0)), false), MARK(s(z0))) A__ADD(s(0), false) -> c3(A__ADD(0, false), MARK(0)) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__PROD_2, A__FACT_1 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c27_1, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1, c24_2, c25_2, c25_1, c26_2, c26_1, c_2, c_1 ---------------------------------------- (183) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (184) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1)))) A__ADD(s(x0), prod(x1, x2)) -> c3(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), prod(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, p(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, s(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, 0)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), prod(x1, true)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(x0)) A__ADD(s(x0), prod(x1, false)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(x0)) A__ADD(s(x0), prod(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(p(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(0, x2)) -> c3(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(true, x2)) -> c3(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(false, x2)) -> c3(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), prod(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2)))) A__ADD(s(x0), p(x1)) -> c3(A__ADD(mark(x0), p(mark(x1))), MARK(x0)) A__ADD(s(x0), p(fact(z0))) -> c3(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), p(zero(z0))) -> c3(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(p(z0))) -> c3(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(add(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(s(z0))) -> c3(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(0)) -> c3(A__ADD(mark(x0), a__p(0)), MARK(x0)) A__ADD(s(x0), p(true)) -> c3(A__ADD(mark(x0), a__p(true)), MARK(x0)) A__ADD(s(x0), p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1)))) A__ADD(s(x0), add(x1, x2)) -> c3(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), add(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), add(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, p(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, s(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, 0)) -> c3(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), add(x1, true)) -> c3(A__ADD(mark(x0), a__add(mark(x1), true)), MARK(x0)) A__ADD(s(x0), add(x1, false)) -> c3(A__ADD(mark(x0), a__add(mark(x1), false)), MARK(x0)) A__ADD(s(x0), add(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), add(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(p(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(s(z0), x2)) -> c3(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(0, x2)) -> c3(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) A__ADD(s(x0), add(true, x2)) -> c3(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(x0)) A__ADD(s(x0), add(false, x2)) -> c3(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), add(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), add(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), add(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__add(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), add(x1, x2)) -> c3(A__ADD(0, a__add(mark(x1), mark(x2)))) A__ADD(s(x0), s(fact(z0))) -> c3(A__ADD(mark(x0), s(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), s(zero(z0))) -> c3(A__ADD(mark(x0), s(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(prod(z0, z1))) -> c3(A__ADD(mark(x0), s(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(p(z0))) -> c3(A__ADD(mark(x0), s(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(add(z0, z1))) -> c3(A__ADD(mark(x0), s(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(s(z0))) -> c3(A__ADD(mark(x0), s(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(0)) -> c3(A__ADD(mark(x0), s(0)), MARK(x0)) A__ADD(s(x0), s(true)) -> c3(A__ADD(mark(x0), s(true)), MARK(x0)) A__ADD(s(x0), s(false)) -> c3(A__ADD(mark(x0), s(false)), MARK(x0)) A__ADD(s(fact(z0)), s(x1)) -> c3(A__ADD(a__fact(mark(z0)), s(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), s(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), s(x1)) -> c3(A__ADD(a__zero(mark(z0)), s(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), s(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), s(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), s(x1)) -> c3(A__ADD(a__p(mark(z0)), s(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), s(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), s(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), s(x1)) -> c3(A__ADD(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__ADD(s(0), s(x1)) -> c3(A__ADD(0, s(mark(x1)))) A__ADD(s(fact(z0)), 0) -> c3(A__ADD(a__fact(mark(z0)), 0), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), 0) -> c3(A__ADD(a__if(mark(z0), z1, z2), 0), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), 0) -> c3(A__ADD(a__zero(mark(z0)), 0), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), 0) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), 0), MARK(prod(z0, z1))) A__ADD(s(p(z0)), 0) -> c3(A__ADD(a__p(mark(z0)), 0), MARK(p(z0))) A__ADD(s(add(z0, z1)), 0) -> c3(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) A__ADD(s(s(z0)), 0) -> c3(A__ADD(s(mark(z0)), 0), MARK(s(z0))) A__ADD(s(0), 0) -> c3(A__ADD(0, 0)) A__ADD(s(fact(z0)), true) -> c3(A__ADD(a__fact(mark(z0)), true), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), true) -> c3(A__ADD(a__if(mark(z0), z1, z2), true), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), true) -> c3(A__ADD(a__zero(mark(z0)), true), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), true) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), true), MARK(prod(z0, z1))) A__ADD(s(p(z0)), true) -> c3(A__ADD(a__p(mark(z0)), true), MARK(p(z0))) A__ADD(s(add(z0, z1)), true) -> c3(A__ADD(a__add(mark(z0), mark(z1)), true), MARK(add(z0, z1))) A__ADD(s(s(z0)), true) -> c3(A__ADD(s(mark(z0)), true), MARK(s(z0))) A__ADD(s(0), true) -> c3(A__ADD(0, true)) A__ADD(s(fact(z0)), false) -> c3(A__ADD(a__fact(mark(z0)), false), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), false) -> c3(A__ADD(a__if(mark(z0), z1, z2), false), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), false) -> c3(A__ADD(a__zero(mark(z0)), false), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), false) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), false), MARK(prod(z0, z1))) A__ADD(s(p(z0)), false) -> c3(A__ADD(a__p(mark(z0)), false), MARK(p(z0))) A__ADD(s(add(z0, z1)), false) -> c3(A__ADD(a__add(mark(z0), mark(z1)), false), MARK(add(z0, z1))) A__ADD(s(s(z0)), false) -> c3(A__ADD(s(mark(z0)), false), MARK(s(z0))) A__ADD(s(0), false) -> c3(A__ADD(0, false)) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), 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MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> 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a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> 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x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1)))) A__ADD(s(x0), prod(x1, x2)) -> c3(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), prod(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, p(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, s(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, 0)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), prod(x1, true)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(x0)) A__ADD(s(x0), prod(x1, false)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(x0)) A__ADD(s(x0), prod(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(p(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(0, x2)) -> c3(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(true, x2)) -> c3(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(false, x2)) -> c3(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), prod(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2)))) A__ADD(s(x0), p(x1)) -> c3(A__ADD(mark(x0), p(mark(x1))), MARK(x0)) A__ADD(s(x0), p(fact(z0))) -> c3(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), p(zero(z0))) -> c3(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(p(z0))) -> c3(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(add(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(s(z0))) -> c3(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(0)) -> c3(A__ADD(mark(x0), a__p(0)), MARK(x0)) A__ADD(s(x0), p(true)) -> c3(A__ADD(mark(x0), a__p(true)), MARK(x0)) A__ADD(s(x0), p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1)))) A__ADD(s(x0), add(x1, x2)) -> c3(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), add(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), add(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, p(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, s(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, 0)) -> c3(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), add(x1, true)) -> c3(A__ADD(mark(x0), a__add(mark(x1), true)), MARK(x0)) A__ADD(s(x0), add(x1, false)) -> c3(A__ADD(mark(x0), a__add(mark(x1), false)), MARK(x0)) A__ADD(s(x0), add(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), add(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(p(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(s(z0), x2)) -> c3(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(0, x2)) -> c3(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) A__ADD(s(x0), add(true, x2)) -> c3(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(x0)) A__ADD(s(x0), add(false, x2)) -> c3(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), add(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), add(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), add(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__add(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), add(x1, x2)) -> c3(A__ADD(0, a__add(mark(x1), mark(x2)))) A__ADD(s(x0), s(fact(z0))) -> c3(A__ADD(mark(x0), s(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), s(zero(z0))) -> c3(A__ADD(mark(x0), s(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(prod(z0, z1))) -> c3(A__ADD(mark(x0), s(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(p(z0))) -> c3(A__ADD(mark(x0), s(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(add(z0, z1))) -> c3(A__ADD(mark(x0), s(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(s(z0))) -> c3(A__ADD(mark(x0), s(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(0)) -> c3(A__ADD(mark(x0), s(0)), MARK(x0)) A__ADD(s(x0), s(true)) -> c3(A__ADD(mark(x0), s(true)), MARK(x0)) A__ADD(s(x0), s(false)) -> c3(A__ADD(mark(x0), s(false)), MARK(x0)) A__ADD(s(fact(z0)), s(x1)) -> c3(A__ADD(a__fact(mark(z0)), s(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), s(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), s(x1)) -> c3(A__ADD(a__zero(mark(z0)), s(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), s(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), s(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), s(x1)) -> c3(A__ADD(a__p(mark(z0)), s(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), s(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), s(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), s(x1)) -> c3(A__ADD(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__ADD(s(0), s(x1)) -> c3(A__ADD(0, s(mark(x1)))) A__ADD(s(fact(z0)), 0) -> c3(A__ADD(a__fact(mark(z0)), 0), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), 0) -> c3(A__ADD(a__if(mark(z0), z1, z2), 0), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), 0) -> c3(A__ADD(a__zero(mark(z0)), 0), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), 0) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), 0), MARK(prod(z0, z1))) A__ADD(s(p(z0)), 0) -> c3(A__ADD(a__p(mark(z0)), 0), MARK(p(z0))) A__ADD(s(add(z0, z1)), 0) -> c3(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) A__ADD(s(s(z0)), 0) -> c3(A__ADD(s(mark(z0)), 0), MARK(s(z0))) A__ADD(s(0), 0) -> c3(A__ADD(0, 0)) A__ADD(s(fact(z0)), true) -> c3(A__ADD(a__fact(mark(z0)), true), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), true) -> c3(A__ADD(a__if(mark(z0), z1, z2), true), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), true) -> c3(A__ADD(a__zero(mark(z0)), true), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), true) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), true), MARK(prod(z0, z1))) A__ADD(s(p(z0)), true) -> c3(A__ADD(a__p(mark(z0)), true), MARK(p(z0))) A__ADD(s(add(z0, z1)), true) -> c3(A__ADD(a__add(mark(z0), mark(z1)), true), MARK(add(z0, z1))) A__ADD(s(s(z0)), true) -> c3(A__ADD(s(mark(z0)), true), MARK(s(z0))) A__ADD(s(0), true) -> c3(A__ADD(0, true)) A__ADD(s(fact(z0)), false) -> c3(A__ADD(a__fact(mark(z0)), false), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), false) -> c3(A__ADD(a__if(mark(z0), z1, z2), false), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), false) -> c3(A__ADD(a__zero(mark(z0)), false), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), false) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), false), MARK(prod(z0, z1))) A__ADD(s(p(z0)), false) -> c3(A__ADD(a__p(mark(z0)), false), MARK(p(z0))) A__ADD(s(add(z0, z1)), false) -> c3(A__ADD(a__add(mark(z0), mark(z1)), false), MARK(add(z0, z1))) A__ADD(s(s(z0)), false) -> c3(A__ADD(s(mark(z0)), false), MARK(s(z0))) A__ADD(s(0), false) -> c3(A__ADD(0, false)) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__PROD_2, A__FACT_1 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c27_1, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1, c24_2, c25_2, c25_1, c26_2, c26_1, c_2, c_1 ---------------------------------------- (185) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__ADD(s(fact(z0)), x1) -> c3(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) by A__ADD(s(fact(x0)), fact(z0)) -> c3(A__ADD(a__fact(mark(x0)), a__fact(mark(z0))), MARK(fact(x0))) A__ADD(s(fact(x0)), if(z0, z1, z2)) -> c3(A__ADD(a__fact(mark(x0)), a__if(mark(z0), z1, z2)), MARK(fact(x0))) A__ADD(s(fact(x0)), zero(z0)) -> c3(A__ADD(a__fact(mark(x0)), a__zero(mark(z0))), MARK(fact(x0))) A__ADD(s(fact(x0)), prod(z0, z1)) -> c3(A__ADD(a__fact(mark(x0)), a__prod(mark(z0), mark(z1))), MARK(fact(x0))) A__ADD(s(fact(x0)), p(z0)) -> c3(A__ADD(a__fact(mark(x0)), a__p(mark(z0))), MARK(fact(x0))) A__ADD(s(fact(x0)), add(z0, z1)) -> c3(A__ADD(a__fact(mark(x0)), a__add(mark(z0), mark(z1))), MARK(fact(x0))) A__ADD(s(fact(x0)), s(z0)) -> c3(A__ADD(a__fact(mark(x0)), s(mark(z0))), MARK(fact(x0))) A__ADD(s(fact(x0)), 0) -> c3(A__ADD(a__fact(mark(x0)), 0), MARK(fact(x0))) A__ADD(s(fact(x0)), true) -> c3(A__ADD(a__fact(mark(x0)), true), MARK(fact(x0))) A__ADD(s(fact(x0)), false) -> c3(A__ADD(a__fact(mark(x0)), false), MARK(fact(x0))) A__ADD(s(fact(x0)), x1) -> c3(A__ADD(a__if(a__zero(mark(mark(x0))), s(0), prod(mark(x0), fact(p(mark(x0))))), mark(x1)), MARK(fact(x0))) A__ADD(s(fact(x0)), x1) -> c3(A__ADD(fact(mark(x0)), mark(x1)), MARK(fact(x0))) A__ADD(s(fact(fact(z0))), x1) -> c3(A__ADD(a__fact(a__fact(mark(z0))), mark(x1)), MARK(fact(fact(z0)))) A__ADD(s(fact(if(z0, z1, z2))), x1) -> c3(A__ADD(a__fact(a__if(mark(z0), z1, z2)), mark(x1)), MARK(fact(if(z0, z1, z2)))) A__ADD(s(fact(zero(z0))), x1) -> c3(A__ADD(a__fact(a__zero(mark(z0))), mark(x1)), MARK(fact(zero(z0)))) A__ADD(s(fact(prod(z0, z1))), x1) -> c3(A__ADD(a__fact(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(fact(prod(z0, z1)))) A__ADD(s(fact(p(z0))), x1) -> c3(A__ADD(a__fact(a__p(mark(z0))), mark(x1)), MARK(fact(p(z0)))) A__ADD(s(fact(add(z0, z1))), x1) -> c3(A__ADD(a__fact(a__add(mark(z0), mark(z1))), mark(x1)), MARK(fact(add(z0, z1)))) A__ADD(s(fact(s(z0))), x1) -> c3(A__ADD(a__fact(s(mark(z0))), mark(x1)), MARK(fact(s(z0)))) A__ADD(s(fact(0)), x1) -> c3(A__ADD(a__fact(0), mark(x1)), MARK(fact(0))) A__ADD(s(fact(true)), x1) -> c3(A__ADD(a__fact(true), mark(x1)), MARK(fact(true))) A__ADD(s(fact(false)), x1) -> c3(A__ADD(a__fact(false), mark(x1)), MARK(fact(false))) A__ADD(s(fact(x0)), x1) -> c3(MARK(fact(x0))) ---------------------------------------- (186) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1)))) A__ADD(s(x0), prod(x1, x2)) -> c3(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), prod(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, p(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, s(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, 0)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), prod(x1, true)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(x0)) A__ADD(s(x0), prod(x1, false)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(x0)) A__ADD(s(x0), prod(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(p(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(0, x2)) -> c3(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(true, x2)) -> c3(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(false, x2)) -> c3(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), prod(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2)))) A__ADD(s(x0), p(x1)) -> c3(A__ADD(mark(x0), p(mark(x1))), MARK(x0)) A__ADD(s(x0), p(fact(z0))) -> c3(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), p(zero(z0))) -> c3(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(p(z0))) -> c3(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(add(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(s(z0))) -> c3(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(0)) -> c3(A__ADD(mark(x0), a__p(0)), MARK(x0)) A__ADD(s(x0), p(true)) -> c3(A__ADD(mark(x0), a__p(true)), MARK(x0)) A__ADD(s(x0), p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1)))) A__ADD(s(x0), add(x1, x2)) -> c3(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), add(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), add(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, p(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, s(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, 0)) -> c3(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), add(x1, true)) -> c3(A__ADD(mark(x0), a__add(mark(x1), true)), MARK(x0)) A__ADD(s(x0), add(x1, false)) -> c3(A__ADD(mark(x0), a__add(mark(x1), false)), MARK(x0)) A__ADD(s(x0), add(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), add(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(p(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(s(z0), x2)) -> c3(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(0, x2)) -> c3(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) A__ADD(s(x0), add(true, x2)) -> c3(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(x0)) A__ADD(s(x0), add(false, x2)) -> c3(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), add(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), add(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), add(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__add(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), add(x1, x2)) -> c3(A__ADD(0, a__add(mark(x1), mark(x2)))) A__ADD(s(x0), s(fact(z0))) -> c3(A__ADD(mark(x0), s(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), s(zero(z0))) -> c3(A__ADD(mark(x0), s(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(prod(z0, z1))) -> c3(A__ADD(mark(x0), s(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(p(z0))) -> c3(A__ADD(mark(x0), s(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(add(z0, z1))) -> c3(A__ADD(mark(x0), s(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(s(z0))) -> c3(A__ADD(mark(x0), s(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(0)) -> c3(A__ADD(mark(x0), s(0)), MARK(x0)) A__ADD(s(x0), s(true)) -> c3(A__ADD(mark(x0), s(true)), MARK(x0)) A__ADD(s(x0), s(false)) -> c3(A__ADD(mark(x0), s(false)), MARK(x0)) A__ADD(s(fact(z0)), s(x1)) -> c3(A__ADD(a__fact(mark(z0)), s(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), s(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), s(x1)) -> c3(A__ADD(a__zero(mark(z0)), s(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), s(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), s(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), s(x1)) -> c3(A__ADD(a__p(mark(z0)), s(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), s(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), s(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), s(x1)) -> c3(A__ADD(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__ADD(s(0), s(x1)) -> c3(A__ADD(0, s(mark(x1)))) A__ADD(s(fact(z0)), 0) -> c3(A__ADD(a__fact(mark(z0)), 0), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), 0) -> c3(A__ADD(a__if(mark(z0), z1, z2), 0), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), 0) -> c3(A__ADD(a__zero(mark(z0)), 0), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), 0) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), 0), MARK(prod(z0, z1))) A__ADD(s(p(z0)), 0) -> c3(A__ADD(a__p(mark(z0)), 0), MARK(p(z0))) A__ADD(s(add(z0, z1)), 0) -> c3(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) A__ADD(s(s(z0)), 0) -> c3(A__ADD(s(mark(z0)), 0), MARK(s(z0))) A__ADD(s(0), 0) -> c3(A__ADD(0, 0)) A__ADD(s(fact(z0)), true) -> c3(A__ADD(a__fact(mark(z0)), true), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), true) -> c3(A__ADD(a__if(mark(z0), z1, z2), true), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), true) -> c3(A__ADD(a__zero(mark(z0)), true), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), true) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), true), MARK(prod(z0, z1))) A__ADD(s(p(z0)), true) -> c3(A__ADD(a__p(mark(z0)), true), MARK(p(z0))) A__ADD(s(add(z0, z1)), true) -> c3(A__ADD(a__add(mark(z0), mark(z1)), true), MARK(add(z0, z1))) A__ADD(s(s(z0)), true) -> c3(A__ADD(s(mark(z0)), true), MARK(s(z0))) A__ADD(s(0), true) -> c3(A__ADD(0, true)) A__ADD(s(fact(z0)), false) -> c3(A__ADD(a__fact(mark(z0)), false), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), false) -> c3(A__ADD(a__if(mark(z0), z1, z2), false), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), false) -> c3(A__ADD(a__zero(mark(z0)), false), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), false) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), false), MARK(prod(z0, z1))) A__ADD(s(p(z0)), false) -> c3(A__ADD(a__p(mark(z0)), false), MARK(p(z0))) A__ADD(s(add(z0, z1)), false) -> c3(A__ADD(a__add(mark(z0), mark(z1)), false), MARK(add(z0, z1))) A__ADD(s(s(z0)), false) -> c3(A__ADD(s(mark(z0)), false), MARK(s(z0))) A__ADD(s(0), false) -> c3(A__ADD(0, false)) A__ADD(s(fact(x0)), x1) -> c3(A__ADD(a__if(a__zero(mark(mark(x0))), s(0), prod(mark(x0), fact(p(mark(x0))))), mark(x1)), MARK(fact(x0))) A__ADD(s(fact(x0)), x1) -> c3(A__ADD(fact(mark(x0)), mark(x1)), MARK(fact(x0))) A__ADD(s(fact(fact(z0))), x1) -> c3(A__ADD(a__fact(a__fact(mark(z0))), mark(x1)), MARK(fact(fact(z0)))) A__ADD(s(fact(if(z0, z1, z2))), x1) -> c3(A__ADD(a__fact(a__if(mark(z0), z1, z2)), mark(x1)), MARK(fact(if(z0, z1, z2)))) A__ADD(s(fact(zero(z0))), x1) -> c3(A__ADD(a__fact(a__zero(mark(z0))), mark(x1)), MARK(fact(zero(z0)))) A__ADD(s(fact(prod(z0, z1))), x1) -> c3(A__ADD(a__fact(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(fact(prod(z0, z1)))) A__ADD(s(fact(p(z0))), x1) -> c3(A__ADD(a__fact(a__p(mark(z0))), mark(x1)), MARK(fact(p(z0)))) A__ADD(s(fact(add(z0, z1))), x1) -> c3(A__ADD(a__fact(a__add(mark(z0), mark(z1))), mark(x1)), MARK(fact(add(z0, z1)))) A__ADD(s(fact(s(z0))), x1) -> c3(A__ADD(a__fact(s(mark(z0))), mark(x1)), MARK(fact(s(z0)))) A__ADD(s(fact(0)), x1) -> c3(A__ADD(a__fact(0), mark(x1)), MARK(fact(0))) A__ADD(s(fact(true)), x1) -> c3(A__ADD(a__fact(true), mark(x1)), MARK(fact(true))) A__ADD(s(fact(false)), x1) -> c3(A__ADD(a__fact(false), mark(x1)), MARK(fact(false))) A__ADD(s(fact(x0)), x1) -> c3(MARK(fact(x0))) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), 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p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1)))) A__ADD(s(x0), add(x1, x2)) -> c3(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), add(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), add(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, p(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, s(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, 0)) -> c3(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), add(x1, true)) -> c3(A__ADD(mark(x0), a__add(mark(x1), true)), MARK(x0)) A__ADD(s(x0), add(x1, false)) -> c3(A__ADD(mark(x0), a__add(mark(x1), false)), MARK(x0)) A__ADD(s(x0), add(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), add(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(p(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(s(z0), x2)) -> c3(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(0, x2)) -> c3(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) A__ADD(s(x0), add(true, x2)) -> c3(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(x0)) A__ADD(s(x0), add(false, x2)) -> c3(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), add(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), add(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), add(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__add(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), add(x1, x2)) -> c3(A__ADD(0, a__add(mark(x1), mark(x2)))) A__ADD(s(x0), s(fact(z0))) -> c3(A__ADD(mark(x0), s(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), s(zero(z0))) -> c3(A__ADD(mark(x0), s(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(prod(z0, z1))) -> c3(A__ADD(mark(x0), s(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(p(z0))) -> c3(A__ADD(mark(x0), s(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(add(z0, z1))) -> c3(A__ADD(mark(x0), s(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(s(z0))) -> c3(A__ADD(mark(x0), s(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(0)) -> c3(A__ADD(mark(x0), s(0)), MARK(x0)) A__ADD(s(x0), s(true)) -> c3(A__ADD(mark(x0), s(true)), MARK(x0)) A__ADD(s(x0), s(false)) -> c3(A__ADD(mark(x0), s(false)), MARK(x0)) A__ADD(s(fact(z0)), s(x1)) -> c3(A__ADD(a__fact(mark(z0)), s(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), s(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), s(x1)) -> c3(A__ADD(a__zero(mark(z0)), s(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), s(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), s(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), s(x1)) -> c3(A__ADD(a__p(mark(z0)), s(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), s(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), s(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), s(x1)) -> c3(A__ADD(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__ADD(s(0), s(x1)) -> c3(A__ADD(0, s(mark(x1)))) A__ADD(s(fact(z0)), 0) -> c3(A__ADD(a__fact(mark(z0)), 0), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), 0) -> c3(A__ADD(a__if(mark(z0), z1, z2), 0), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), 0) -> c3(A__ADD(a__zero(mark(z0)), 0), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), 0) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), 0), MARK(prod(z0, z1))) A__ADD(s(p(z0)), 0) -> c3(A__ADD(a__p(mark(z0)), 0), MARK(p(z0))) A__ADD(s(add(z0, z1)), 0) -> c3(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) A__ADD(s(s(z0)), 0) -> c3(A__ADD(s(mark(z0)), 0), MARK(s(z0))) A__ADD(s(0), 0) -> c3(A__ADD(0, 0)) A__ADD(s(fact(z0)), true) -> c3(A__ADD(a__fact(mark(z0)), true), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), true) -> c3(A__ADD(a__if(mark(z0), z1, z2), true), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), true) -> c3(A__ADD(a__zero(mark(z0)), true), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), true) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), true), MARK(prod(z0, z1))) A__ADD(s(p(z0)), true) -> c3(A__ADD(a__p(mark(z0)), true), MARK(p(z0))) A__ADD(s(add(z0, z1)), true) -> c3(A__ADD(a__add(mark(z0), mark(z1)), true), MARK(add(z0, z1))) A__ADD(s(s(z0)), true) -> c3(A__ADD(s(mark(z0)), true), MARK(s(z0))) A__ADD(s(0), true) -> c3(A__ADD(0, true)) A__ADD(s(fact(z0)), false) -> c3(A__ADD(a__fact(mark(z0)), false), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), false) -> c3(A__ADD(a__if(mark(z0), z1, z2), false), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), false) -> c3(A__ADD(a__zero(mark(z0)), false), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), false) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), false), MARK(prod(z0, z1))) A__ADD(s(p(z0)), false) -> c3(A__ADD(a__p(mark(z0)), false), MARK(p(z0))) A__ADD(s(add(z0, z1)), false) -> c3(A__ADD(a__add(mark(z0), mark(z1)), false), MARK(add(z0, z1))) A__ADD(s(s(z0)), false) -> c3(A__ADD(s(mark(z0)), false), MARK(s(z0))) A__ADD(s(0), false) -> c3(A__ADD(0, false)) A__ADD(s(fact(x0)), x1) -> c3(A__ADD(a__if(a__zero(mark(mark(x0))), s(0), prod(mark(x0), fact(p(mark(x0))))), mark(x1)), MARK(fact(x0))) A__ADD(s(fact(x0)), x1) -> c3(A__ADD(fact(mark(x0)), mark(x1)), MARK(fact(x0))) A__ADD(s(fact(fact(z0))), x1) -> c3(A__ADD(a__fact(a__fact(mark(z0))), mark(x1)), MARK(fact(fact(z0)))) A__ADD(s(fact(if(z0, z1, z2))), x1) -> c3(A__ADD(a__fact(a__if(mark(z0), z1, z2)), mark(x1)), MARK(fact(if(z0, z1, z2)))) A__ADD(s(fact(zero(z0))), x1) -> c3(A__ADD(a__fact(a__zero(mark(z0))), mark(x1)), MARK(fact(zero(z0)))) A__ADD(s(fact(prod(z0, z1))), x1) -> c3(A__ADD(a__fact(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(fact(prod(z0, z1)))) A__ADD(s(fact(p(z0))), x1) -> c3(A__ADD(a__fact(a__p(mark(z0))), mark(x1)), MARK(fact(p(z0)))) A__ADD(s(fact(add(z0, z1))), x1) -> c3(A__ADD(a__fact(a__add(mark(z0), mark(z1))), mark(x1)), MARK(fact(add(z0, z1)))) A__ADD(s(fact(s(z0))), x1) -> c3(A__ADD(a__fact(s(mark(z0))), mark(x1)), MARK(fact(s(z0)))) A__ADD(s(fact(0)), x1) -> c3(A__ADD(a__fact(0), mark(x1)), MARK(fact(0))) A__ADD(s(fact(true)), x1) -> c3(A__ADD(a__fact(true), mark(x1)), MARK(fact(true))) A__ADD(s(fact(false)), x1) -> c3(A__ADD(a__fact(false), mark(x1)), MARK(fact(false))) A__ADD(s(fact(x0)), x1) -> c3(MARK(fact(x0))) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__PROD_2, A__FACT_1 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c27_1, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1, c24_2, c25_2, c25_1, c26_2, c26_1, c_2, c_1 ---------------------------------------- (187) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (188) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> 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A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), 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z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2)))) A__ADD(s(x0), p(x1)) -> c3(A__ADD(mark(x0), p(mark(x1))), MARK(x0)) A__ADD(s(x0), p(fact(z0))) -> c3(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), p(zero(z0))) -> c3(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(p(z0))) -> c3(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(add(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(s(z0))) -> c3(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(0)) -> c3(A__ADD(mark(x0), a__p(0)), MARK(x0)) A__ADD(s(x0), p(true)) -> c3(A__ADD(mark(x0), a__p(true)), MARK(x0)) A__ADD(s(x0), p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1)))) A__ADD(s(x0), add(x1, x2)) -> c3(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), add(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), add(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, p(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, s(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, 0)) -> c3(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), add(x1, true)) -> c3(A__ADD(mark(x0), a__add(mark(x1), true)), MARK(x0)) A__ADD(s(x0), add(x1, false)) -> c3(A__ADD(mark(x0), a__add(mark(x1), false)), MARK(x0)) A__ADD(s(x0), add(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), add(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(p(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(s(z0), x2)) -> c3(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(0, x2)) -> c3(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) A__ADD(s(x0), add(true, x2)) -> c3(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(x0)) A__ADD(s(x0), add(false, x2)) -> c3(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), add(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), add(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), add(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__add(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), add(x1, x2)) -> c3(A__ADD(0, a__add(mark(x1), mark(x2)))) A__ADD(s(x0), s(fact(z0))) -> c3(A__ADD(mark(x0), s(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), s(zero(z0))) -> c3(A__ADD(mark(x0), s(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(prod(z0, z1))) -> c3(A__ADD(mark(x0), s(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(p(z0))) -> c3(A__ADD(mark(x0), s(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(add(z0, z1))) -> c3(A__ADD(mark(x0), s(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(s(z0))) -> c3(A__ADD(mark(x0), s(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(0)) -> c3(A__ADD(mark(x0), s(0)), MARK(x0)) A__ADD(s(x0), s(true)) -> c3(A__ADD(mark(x0), s(true)), MARK(x0)) A__ADD(s(x0), s(false)) -> c3(A__ADD(mark(x0), s(false)), MARK(x0)) A__ADD(s(fact(z0)), s(x1)) -> c3(A__ADD(a__fact(mark(z0)), s(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), s(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), s(x1)) -> c3(A__ADD(a__zero(mark(z0)), s(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), s(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), s(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), s(x1)) -> c3(A__ADD(a__p(mark(z0)), s(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), s(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), s(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), s(x1)) -> c3(A__ADD(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__ADD(s(0), s(x1)) -> c3(A__ADD(0, s(mark(x1)))) A__ADD(s(fact(z0)), 0) -> c3(A__ADD(a__fact(mark(z0)), 0), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), 0) -> c3(A__ADD(a__if(mark(z0), z1, z2), 0), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), 0) -> c3(A__ADD(a__zero(mark(z0)), 0), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), 0) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), 0), MARK(prod(z0, z1))) A__ADD(s(p(z0)), 0) -> c3(A__ADD(a__p(mark(z0)), 0), MARK(p(z0))) A__ADD(s(add(z0, z1)), 0) -> c3(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) A__ADD(s(s(z0)), 0) -> c3(A__ADD(s(mark(z0)), 0), MARK(s(z0))) A__ADD(s(0), 0) -> c3(A__ADD(0, 0)) A__ADD(s(fact(z0)), true) -> c3(A__ADD(a__fact(mark(z0)), true), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), true) -> c3(A__ADD(a__if(mark(z0), z1, z2), true), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), true) -> c3(A__ADD(a__zero(mark(z0)), true), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), true) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), true), MARK(prod(z0, z1))) A__ADD(s(p(z0)), true) -> c3(A__ADD(a__p(mark(z0)), true), MARK(p(z0))) A__ADD(s(add(z0, z1)), true) -> c3(A__ADD(a__add(mark(z0), mark(z1)), true), MARK(add(z0, z1))) A__ADD(s(s(z0)), true) -> c3(A__ADD(s(mark(z0)), true), MARK(s(z0))) A__ADD(s(0), true) -> c3(A__ADD(0, true)) A__ADD(s(fact(z0)), false) -> c3(A__ADD(a__fact(mark(z0)), false), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), false) -> c3(A__ADD(a__if(mark(z0), z1, z2), false), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), false) -> c3(A__ADD(a__zero(mark(z0)), false), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), false) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), false), MARK(prod(z0, z1))) A__ADD(s(p(z0)), false) -> c3(A__ADD(a__p(mark(z0)), false), MARK(p(z0))) A__ADD(s(add(z0, z1)), false) -> c3(A__ADD(a__add(mark(z0), mark(z1)), false), MARK(add(z0, z1))) A__ADD(s(s(z0)), false) -> c3(A__ADD(s(mark(z0)), false), MARK(s(z0))) A__ADD(s(0), false) -> c3(A__ADD(0, false)) A__ADD(s(fact(x0)), x1) -> c3(A__ADD(a__if(a__zero(mark(mark(x0))), s(0), prod(mark(x0), fact(p(mark(x0))))), mark(x1)), MARK(fact(x0))) A__ADD(s(fact(fact(z0))), x1) -> c3(A__ADD(a__fact(a__fact(mark(z0))), mark(x1)), MARK(fact(fact(z0)))) A__ADD(s(fact(if(z0, z1, z2))), x1) -> c3(A__ADD(a__fact(a__if(mark(z0), z1, z2)), mark(x1)), MARK(fact(if(z0, z1, z2)))) A__ADD(s(fact(zero(z0))), x1) -> c3(A__ADD(a__fact(a__zero(mark(z0))), mark(x1)), MARK(fact(zero(z0)))) A__ADD(s(fact(prod(z0, z1))), x1) -> c3(A__ADD(a__fact(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(fact(prod(z0, z1)))) A__ADD(s(fact(p(z0))), x1) -> c3(A__ADD(a__fact(a__p(mark(z0))), mark(x1)), MARK(fact(p(z0)))) A__ADD(s(fact(add(z0, z1))), x1) -> c3(A__ADD(a__fact(a__add(mark(z0), mark(z1))), mark(x1)), MARK(fact(add(z0, z1)))) A__ADD(s(fact(s(z0))), x1) -> c3(A__ADD(a__fact(s(mark(z0))), mark(x1)), MARK(fact(s(z0)))) A__ADD(s(fact(0)), x1) -> c3(A__ADD(a__fact(0), mark(x1)), MARK(fact(0))) A__ADD(s(fact(true)), x1) -> c3(A__ADD(a__fact(true), mark(x1)), MARK(fact(true))) A__ADD(s(fact(false)), x1) -> c3(A__ADD(a__fact(false), mark(x1)), MARK(fact(false))) A__ADD(s(fact(x0)), x1) -> c3(MARK(fact(x0))) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), 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MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), 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A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), prod(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, p(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, s(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, 0)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), prod(x1, true)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(x0)) A__ADD(s(x0), prod(x1, false)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(x0)) A__ADD(s(x0), prod(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(p(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(0, x2)) -> c3(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(true, x2)) -> c3(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(false, x2)) -> c3(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), prod(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2)))) A__ADD(s(x0), p(x1)) -> c3(A__ADD(mark(x0), p(mark(x1))), MARK(x0)) A__ADD(s(x0), p(fact(z0))) -> c3(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), p(zero(z0))) -> c3(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(p(z0))) -> c3(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(add(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(s(z0))) -> c3(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(0)) -> c3(A__ADD(mark(x0), a__p(0)), MARK(x0)) A__ADD(s(x0), p(true)) -> c3(A__ADD(mark(x0), a__p(true)), MARK(x0)) A__ADD(s(x0), p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1)))) A__ADD(s(x0), add(x1, x2)) -> c3(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), add(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), add(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, p(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, s(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, 0)) -> c3(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), add(x1, true)) -> c3(A__ADD(mark(x0), a__add(mark(x1), true)), MARK(x0)) A__ADD(s(x0), add(x1, false)) -> c3(A__ADD(mark(x0), a__add(mark(x1), false)), MARK(x0)) A__ADD(s(x0), add(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), add(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(p(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(s(z0), x2)) -> c3(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(0, x2)) -> c3(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) A__ADD(s(x0), add(true, x2)) -> c3(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(x0)) A__ADD(s(x0), add(false, x2)) -> c3(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), add(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), add(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), add(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__add(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), add(x1, x2)) -> c3(A__ADD(0, a__add(mark(x1), mark(x2)))) A__ADD(s(x0), s(fact(z0))) -> c3(A__ADD(mark(x0), s(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), s(zero(z0))) -> c3(A__ADD(mark(x0), s(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(prod(z0, z1))) -> c3(A__ADD(mark(x0), s(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(p(z0))) -> c3(A__ADD(mark(x0), s(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(add(z0, z1))) -> c3(A__ADD(mark(x0), s(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(s(z0))) -> c3(A__ADD(mark(x0), s(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(0)) -> c3(A__ADD(mark(x0), s(0)), MARK(x0)) A__ADD(s(x0), s(true)) -> c3(A__ADD(mark(x0), s(true)), MARK(x0)) A__ADD(s(x0), s(false)) -> c3(A__ADD(mark(x0), s(false)), MARK(x0)) A__ADD(s(fact(z0)), s(x1)) -> c3(A__ADD(a__fact(mark(z0)), s(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), s(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), s(x1)) -> c3(A__ADD(a__zero(mark(z0)), s(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), s(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), s(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), s(x1)) -> c3(A__ADD(a__p(mark(z0)), s(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), s(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), s(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), s(x1)) -> c3(A__ADD(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__ADD(s(0), s(x1)) -> c3(A__ADD(0, s(mark(x1)))) A__ADD(s(fact(z0)), 0) -> c3(A__ADD(a__fact(mark(z0)), 0), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), 0) -> c3(A__ADD(a__if(mark(z0), z1, z2), 0), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), 0) -> c3(A__ADD(a__zero(mark(z0)), 0), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), 0) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), 0), MARK(prod(z0, z1))) A__ADD(s(p(z0)), 0) -> c3(A__ADD(a__p(mark(z0)), 0), MARK(p(z0))) A__ADD(s(add(z0, z1)), 0) -> c3(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) A__ADD(s(s(z0)), 0) -> c3(A__ADD(s(mark(z0)), 0), MARK(s(z0))) A__ADD(s(0), 0) -> c3(A__ADD(0, 0)) A__ADD(s(fact(z0)), true) -> c3(A__ADD(a__fact(mark(z0)), true), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), true) -> c3(A__ADD(a__if(mark(z0), z1, z2), true), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), true) -> c3(A__ADD(a__zero(mark(z0)), true), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), true) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), true), MARK(prod(z0, z1))) A__ADD(s(p(z0)), true) -> c3(A__ADD(a__p(mark(z0)), true), MARK(p(z0))) A__ADD(s(add(z0, z1)), true) -> c3(A__ADD(a__add(mark(z0), mark(z1)), true), MARK(add(z0, z1))) A__ADD(s(s(z0)), true) -> c3(A__ADD(s(mark(z0)), true), MARK(s(z0))) A__ADD(s(0), true) -> c3(A__ADD(0, true)) A__ADD(s(fact(z0)), false) -> c3(A__ADD(a__fact(mark(z0)), false), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), false) -> c3(A__ADD(a__if(mark(z0), z1, z2), false), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), false) -> c3(A__ADD(a__zero(mark(z0)), false), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), false) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), false), MARK(prod(z0, z1))) A__ADD(s(p(z0)), false) -> c3(A__ADD(a__p(mark(z0)), false), MARK(p(z0))) A__ADD(s(add(z0, z1)), false) -> c3(A__ADD(a__add(mark(z0), mark(z1)), false), MARK(add(z0, z1))) A__ADD(s(s(z0)), false) -> c3(A__ADD(s(mark(z0)), false), MARK(s(z0))) A__ADD(s(0), false) -> c3(A__ADD(0, false)) A__ADD(s(fact(x0)), x1) -> c3(A__ADD(a__if(a__zero(mark(mark(x0))), s(0), prod(mark(x0), fact(p(mark(x0))))), mark(x1)), MARK(fact(x0))) A__ADD(s(fact(fact(z0))), x1) -> c3(A__ADD(a__fact(a__fact(mark(z0))), mark(x1)), MARK(fact(fact(z0)))) A__ADD(s(fact(if(z0, z1, z2))), x1) -> c3(A__ADD(a__fact(a__if(mark(z0), z1, z2)), mark(x1)), MARK(fact(if(z0, z1, z2)))) A__ADD(s(fact(zero(z0))), x1) -> c3(A__ADD(a__fact(a__zero(mark(z0))), mark(x1)), MARK(fact(zero(z0)))) A__ADD(s(fact(prod(z0, z1))), x1) -> c3(A__ADD(a__fact(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(fact(prod(z0, z1)))) A__ADD(s(fact(p(z0))), x1) -> c3(A__ADD(a__fact(a__p(mark(z0))), mark(x1)), MARK(fact(p(z0)))) A__ADD(s(fact(add(z0, z1))), x1) -> c3(A__ADD(a__fact(a__add(mark(z0), mark(z1))), mark(x1)), MARK(fact(add(z0, z1)))) A__ADD(s(fact(s(z0))), x1) -> c3(A__ADD(a__fact(s(mark(z0))), mark(x1)), MARK(fact(s(z0)))) A__ADD(s(fact(0)), x1) -> c3(A__ADD(a__fact(0), mark(x1)), MARK(fact(0))) A__ADD(s(fact(true)), x1) -> c3(A__ADD(a__fact(true), mark(x1)), MARK(fact(true))) A__ADD(s(fact(false)), x1) -> c3(A__ADD(a__fact(false), mark(x1)), MARK(fact(false))) A__ADD(s(fact(x0)), x1) -> c3(MARK(fact(x0))) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__PROD_2, A__FACT_1 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c27_1, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1, c24_2, c25_2, c25_1, c26_2, c26_1, c_2, c_1 ---------------------------------------- (189) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__ADD(s(if(z0, z1, z2)), x1) -> c3(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) by A__ADD(s(if(x0, x1, x2)), fact(z0)) -> c3(A__ADD(a__if(mark(x0), x1, x2), a__fact(mark(z0))), MARK(if(x0, x1, x2))) A__ADD(s(if(x0, x1, x2)), if(z0, z1, z2)) -> c3(A__ADD(a__if(mark(x0), x1, x2), a__if(mark(z0), z1, z2)), MARK(if(x0, x1, x2))) A__ADD(s(if(x0, x1, x2)), zero(z0)) -> c3(A__ADD(a__if(mark(x0), x1, x2), a__zero(mark(z0))), MARK(if(x0, x1, x2))) A__ADD(s(if(x0, x1, x2)), prod(z0, z1)) -> c3(A__ADD(a__if(mark(x0), x1, x2), a__prod(mark(z0), mark(z1))), MARK(if(x0, x1, x2))) A__ADD(s(if(x0, x1, x2)), p(z0)) -> c3(A__ADD(a__if(mark(x0), x1, x2), a__p(mark(z0))), MARK(if(x0, x1, x2))) A__ADD(s(if(x0, x1, x2)), add(z0, z1)) -> c3(A__ADD(a__if(mark(x0), x1, x2), a__add(mark(z0), mark(z1))), MARK(if(x0, x1, x2))) A__ADD(s(if(x0, x1, x2)), s(z0)) -> c3(A__ADD(a__if(mark(x0), x1, x2), s(mark(z0))), MARK(if(x0, x1, x2))) A__ADD(s(if(x0, x1, x2)), 0) -> c3(A__ADD(a__if(mark(x0), x1, x2), 0), MARK(if(x0, x1, x2))) A__ADD(s(if(x0, x1, x2)), true) -> c3(A__ADD(a__if(mark(x0), x1, x2), true), MARK(if(x0, x1, x2))) A__ADD(s(if(x0, x1, x2)), false) -> c3(A__ADD(a__if(mark(x0), x1, x2), false), MARK(if(x0, x1, x2))) A__ADD(s(if(x0, z1, z2)), x3) -> c3(A__ADD(if(mark(x0), z1, z2), mark(x3)), MARK(if(x0, z1, z2))) A__ADD(s(if(fact(z0), x1, x2)), x3) -> c3(A__ADD(a__if(a__fact(mark(z0)), x1, x2), mark(x3)), MARK(if(fact(z0), x1, x2))) A__ADD(s(if(if(z0, z1, z2), x1, x2)), x3) -> c3(A__ADD(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(if(if(z0, z1, z2), x1, x2))) A__ADD(s(if(zero(z0), x1, x2)), x3) -> c3(A__ADD(a__if(a__zero(mark(z0)), x1, x2), mark(x3)), MARK(if(zero(z0), x1, x2))) A__ADD(s(if(prod(z0, z1), x1, x2)), x3) -> c3(A__ADD(a__if(a__prod(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(prod(z0, z1), x1, x2))) A__ADD(s(if(p(z0), x1, x2)), x3) -> c3(A__ADD(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(if(p(z0), x1, x2))) A__ADD(s(if(add(z0, z1), x1, x2)), x3) -> c3(A__ADD(a__if(a__add(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(add(z0, z1), x1, x2))) A__ADD(s(if(s(z0), x1, x2)), x3) -> c3(A__ADD(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(if(s(z0), x1, x2))) A__ADD(s(if(0, x1, x2)), x3) -> c3(A__ADD(a__if(0, x1, x2), mark(x3)), MARK(if(0, x1, x2))) A__ADD(s(if(true, x1, x2)), x3) -> c3(A__ADD(a__if(true, x1, x2), mark(x3)), MARK(if(true, x1, x2))) A__ADD(s(if(false, x1, x2)), x3) -> c3(A__ADD(a__if(false, x1, x2), mark(x3)), MARK(if(false, x1, x2))) ---------------------------------------- (190) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1)))) A__ADD(s(x0), prod(x1, x2)) -> c3(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), prod(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, p(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, s(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, 0)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), prod(x1, true)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(x0)) A__ADD(s(x0), prod(x1, false)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(x0)) A__ADD(s(x0), prod(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(p(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(0, x2)) -> c3(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(true, x2)) -> c3(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(false, x2)) -> c3(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), prod(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2)))) A__ADD(s(x0), p(x1)) -> c3(A__ADD(mark(x0), p(mark(x1))), MARK(x0)) A__ADD(s(x0), p(fact(z0))) -> c3(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), p(zero(z0))) -> c3(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(p(z0))) -> c3(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(add(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(s(z0))) -> c3(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(0)) -> c3(A__ADD(mark(x0), a__p(0)), MARK(x0)) A__ADD(s(x0), p(true)) -> c3(A__ADD(mark(x0), a__p(true)), MARK(x0)) A__ADD(s(x0), p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1)))) A__ADD(s(x0), add(x1, x2)) -> c3(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), add(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), add(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, p(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, s(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, 0)) -> c3(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), add(x1, true)) -> c3(A__ADD(mark(x0), a__add(mark(x1), true)), MARK(x0)) A__ADD(s(x0), add(x1, false)) -> c3(A__ADD(mark(x0), a__add(mark(x1), false)), MARK(x0)) A__ADD(s(x0), add(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), add(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(p(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(s(z0), x2)) -> c3(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(0, x2)) -> c3(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) A__ADD(s(x0), add(true, x2)) -> c3(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(x0)) A__ADD(s(x0), add(false, x2)) -> c3(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), add(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), add(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), add(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__add(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), add(x1, x2)) -> c3(A__ADD(0, a__add(mark(x1), mark(x2)))) A__ADD(s(x0), s(fact(z0))) -> c3(A__ADD(mark(x0), s(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), s(zero(z0))) -> c3(A__ADD(mark(x0), s(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(prod(z0, z1))) -> c3(A__ADD(mark(x0), s(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(p(z0))) -> c3(A__ADD(mark(x0), s(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(add(z0, z1))) -> c3(A__ADD(mark(x0), s(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(s(z0))) -> c3(A__ADD(mark(x0), s(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(0)) -> c3(A__ADD(mark(x0), s(0)), MARK(x0)) A__ADD(s(x0), s(true)) -> c3(A__ADD(mark(x0), s(true)), MARK(x0)) A__ADD(s(x0), s(false)) -> c3(A__ADD(mark(x0), s(false)), MARK(x0)) A__ADD(s(fact(z0)), s(x1)) -> c3(A__ADD(a__fact(mark(z0)), s(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), s(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), s(x1)) -> c3(A__ADD(a__zero(mark(z0)), s(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), s(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), s(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), s(x1)) -> c3(A__ADD(a__p(mark(z0)), s(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), s(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), s(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), s(x1)) -> c3(A__ADD(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__ADD(s(0), s(x1)) -> c3(A__ADD(0, s(mark(x1)))) A__ADD(s(fact(z0)), 0) -> c3(A__ADD(a__fact(mark(z0)), 0), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), 0) -> c3(A__ADD(a__if(mark(z0), z1, z2), 0), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), 0) -> c3(A__ADD(a__zero(mark(z0)), 0), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), 0) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), 0), MARK(prod(z0, z1))) A__ADD(s(p(z0)), 0) -> c3(A__ADD(a__p(mark(z0)), 0), MARK(p(z0))) A__ADD(s(add(z0, z1)), 0) -> c3(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) A__ADD(s(s(z0)), 0) -> c3(A__ADD(s(mark(z0)), 0), MARK(s(z0))) A__ADD(s(0), 0) -> c3(A__ADD(0, 0)) A__ADD(s(fact(z0)), true) -> c3(A__ADD(a__fact(mark(z0)), true), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), true) -> c3(A__ADD(a__if(mark(z0), z1, z2), true), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), true) -> c3(A__ADD(a__zero(mark(z0)), true), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), true) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), true), MARK(prod(z0, z1))) A__ADD(s(p(z0)), true) -> c3(A__ADD(a__p(mark(z0)), true), MARK(p(z0))) A__ADD(s(add(z0, z1)), true) -> c3(A__ADD(a__add(mark(z0), mark(z1)), true), MARK(add(z0, z1))) A__ADD(s(s(z0)), true) -> c3(A__ADD(s(mark(z0)), true), MARK(s(z0))) A__ADD(s(0), true) -> c3(A__ADD(0, true)) A__ADD(s(fact(z0)), false) -> c3(A__ADD(a__fact(mark(z0)), false), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), false) -> c3(A__ADD(a__if(mark(z0), z1, z2), false), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), false) -> c3(A__ADD(a__zero(mark(z0)), false), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), false) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), false), MARK(prod(z0, z1))) A__ADD(s(p(z0)), false) -> c3(A__ADD(a__p(mark(z0)), false), MARK(p(z0))) A__ADD(s(add(z0, z1)), false) -> c3(A__ADD(a__add(mark(z0), mark(z1)), false), MARK(add(z0, z1))) A__ADD(s(s(z0)), false) -> c3(A__ADD(s(mark(z0)), false), MARK(s(z0))) A__ADD(s(0), false) -> c3(A__ADD(0, false)) A__ADD(s(fact(x0)), x1) -> c3(A__ADD(a__if(a__zero(mark(mark(x0))), s(0), prod(mark(x0), fact(p(mark(x0))))), mark(x1)), MARK(fact(x0))) A__ADD(s(fact(fact(z0))), x1) -> c3(A__ADD(a__fact(a__fact(mark(z0))), mark(x1)), MARK(fact(fact(z0)))) A__ADD(s(fact(if(z0, z1, z2))), x1) -> c3(A__ADD(a__fact(a__if(mark(z0), z1, z2)), mark(x1)), MARK(fact(if(z0, z1, z2)))) A__ADD(s(fact(zero(z0))), x1) -> c3(A__ADD(a__fact(a__zero(mark(z0))), mark(x1)), MARK(fact(zero(z0)))) A__ADD(s(fact(prod(z0, z1))), x1) -> c3(A__ADD(a__fact(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(fact(prod(z0, z1)))) A__ADD(s(fact(p(z0))), x1) -> c3(A__ADD(a__fact(a__p(mark(z0))), mark(x1)), MARK(fact(p(z0)))) A__ADD(s(fact(add(z0, z1))), x1) -> c3(A__ADD(a__fact(a__add(mark(z0), mark(z1))), mark(x1)), MARK(fact(add(z0, z1)))) A__ADD(s(fact(s(z0))), x1) -> c3(A__ADD(a__fact(s(mark(z0))), mark(x1)), MARK(fact(s(z0)))) A__ADD(s(fact(0)), x1) -> c3(A__ADD(a__fact(0), mark(x1)), MARK(fact(0))) A__ADD(s(fact(true)), x1) -> c3(A__ADD(a__fact(true), mark(x1)), MARK(fact(true))) A__ADD(s(fact(false)), x1) -> c3(A__ADD(a__fact(false), mark(x1)), MARK(fact(false))) A__ADD(s(fact(x0)), x1) -> c3(MARK(fact(x0))) A__ADD(s(if(x0, z1, z2)), x3) -> c3(A__ADD(if(mark(x0), z1, z2), mark(x3)), MARK(if(x0, z1, z2))) A__ADD(s(if(fact(z0), x1, x2)), x3) -> c3(A__ADD(a__if(a__fact(mark(z0)), x1, x2), mark(x3)), MARK(if(fact(z0), x1, x2))) A__ADD(s(if(if(z0, z1, z2), x1, x2)), x3) -> c3(A__ADD(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(if(if(z0, z1, z2), x1, x2))) A__ADD(s(if(zero(z0), x1, x2)), x3) -> c3(A__ADD(a__if(a__zero(mark(z0)), x1, x2), mark(x3)), MARK(if(zero(z0), x1, x2))) A__ADD(s(if(prod(z0, z1), x1, x2)), x3) -> c3(A__ADD(a__if(a__prod(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(prod(z0, z1), x1, x2))) A__ADD(s(if(p(z0), x1, x2)), x3) -> c3(A__ADD(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(if(p(z0), x1, x2))) A__ADD(s(if(add(z0, z1), x1, x2)), x3) -> c3(A__ADD(a__if(a__add(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(add(z0, z1), x1, x2))) A__ADD(s(if(s(z0), x1, x2)), x3) -> c3(A__ADD(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(if(s(z0), x1, x2))) A__ADD(s(if(0, x1, x2)), x3) -> c3(A__ADD(a__if(0, x1, x2), mark(x3)), MARK(if(0, x1, x2))) A__ADD(s(if(true, x1, x2)), x3) -> c3(A__ADD(a__if(true, x1, x2), mark(x3)), MARK(if(true, x1, x2))) A__ADD(s(if(false, x1, x2)), x3) -> c3(A__ADD(a__if(false, x1, x2), mark(x3)), MARK(if(false, x1, x2))) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) 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x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(0, x2)) -> c3(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(true, x2)) -> c3(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(false, x2)) -> c3(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), prod(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2)))) A__ADD(s(x0), p(x1)) -> c3(A__ADD(mark(x0), p(mark(x1))), MARK(x0)) A__ADD(s(x0), p(fact(z0))) -> c3(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), p(zero(z0))) -> c3(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(p(z0))) -> c3(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(add(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(s(z0))) -> c3(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(0)) -> c3(A__ADD(mark(x0), a__p(0)), MARK(x0)) A__ADD(s(x0), p(true)) -> c3(A__ADD(mark(x0), a__p(true)), MARK(x0)) A__ADD(s(x0), p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1)))) A__ADD(s(x0), add(x1, x2)) -> c3(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), add(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), add(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, p(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, s(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, 0)) -> c3(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), add(x1, true)) -> c3(A__ADD(mark(x0), a__add(mark(x1), true)), MARK(x0)) A__ADD(s(x0), add(x1, false)) -> c3(A__ADD(mark(x0), a__add(mark(x1), false)), MARK(x0)) A__ADD(s(x0), add(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), add(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(p(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(s(z0), x2)) -> c3(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(0, x2)) -> c3(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) A__ADD(s(x0), add(true, x2)) -> c3(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(x0)) A__ADD(s(x0), add(false, x2)) -> c3(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), add(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), add(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), add(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__add(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), add(x1, x2)) -> c3(A__ADD(0, a__add(mark(x1), mark(x2)))) A__ADD(s(x0), s(fact(z0))) -> c3(A__ADD(mark(x0), s(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), s(zero(z0))) -> c3(A__ADD(mark(x0), s(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(prod(z0, z1))) -> c3(A__ADD(mark(x0), s(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(p(z0))) -> c3(A__ADD(mark(x0), s(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(add(z0, z1))) -> c3(A__ADD(mark(x0), s(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(s(z0))) -> c3(A__ADD(mark(x0), s(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(0)) -> c3(A__ADD(mark(x0), s(0)), MARK(x0)) A__ADD(s(x0), s(true)) -> c3(A__ADD(mark(x0), s(true)), MARK(x0)) A__ADD(s(x0), s(false)) -> c3(A__ADD(mark(x0), s(false)), MARK(x0)) A__ADD(s(fact(z0)), s(x1)) -> c3(A__ADD(a__fact(mark(z0)), s(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), s(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), s(x1)) -> c3(A__ADD(a__zero(mark(z0)), s(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), s(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), s(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), s(x1)) -> c3(A__ADD(a__p(mark(z0)), s(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), s(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), s(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), s(x1)) -> c3(A__ADD(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__ADD(s(0), s(x1)) -> c3(A__ADD(0, s(mark(x1)))) A__ADD(s(fact(z0)), 0) -> c3(A__ADD(a__fact(mark(z0)), 0), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), 0) -> c3(A__ADD(a__if(mark(z0), z1, z2), 0), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), 0) -> c3(A__ADD(a__zero(mark(z0)), 0), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), 0) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), 0), MARK(prod(z0, z1))) A__ADD(s(p(z0)), 0) -> c3(A__ADD(a__p(mark(z0)), 0), MARK(p(z0))) A__ADD(s(add(z0, z1)), 0) -> c3(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) A__ADD(s(s(z0)), 0) -> c3(A__ADD(s(mark(z0)), 0), MARK(s(z0))) A__ADD(s(0), 0) -> c3(A__ADD(0, 0)) A__ADD(s(fact(z0)), true) -> c3(A__ADD(a__fact(mark(z0)), true), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), true) -> c3(A__ADD(a__if(mark(z0), z1, z2), true), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), true) -> c3(A__ADD(a__zero(mark(z0)), true), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), true) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), true), MARK(prod(z0, z1))) A__ADD(s(p(z0)), true) -> c3(A__ADD(a__p(mark(z0)), true), MARK(p(z0))) A__ADD(s(add(z0, z1)), true) -> c3(A__ADD(a__add(mark(z0), mark(z1)), true), MARK(add(z0, z1))) A__ADD(s(s(z0)), true) -> c3(A__ADD(s(mark(z0)), true), MARK(s(z0))) A__ADD(s(0), true) -> c3(A__ADD(0, true)) A__ADD(s(fact(z0)), false) -> c3(A__ADD(a__fact(mark(z0)), false), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), false) -> c3(A__ADD(a__if(mark(z0), z1, z2), false), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), false) -> c3(A__ADD(a__zero(mark(z0)), false), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), false) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), false), MARK(prod(z0, z1))) A__ADD(s(p(z0)), false) -> c3(A__ADD(a__p(mark(z0)), false), MARK(p(z0))) A__ADD(s(add(z0, z1)), false) -> c3(A__ADD(a__add(mark(z0), mark(z1)), false), MARK(add(z0, z1))) A__ADD(s(s(z0)), false) -> c3(A__ADD(s(mark(z0)), false), MARK(s(z0))) A__ADD(s(0), false) -> c3(A__ADD(0, false)) A__ADD(s(fact(x0)), x1) -> c3(A__ADD(a__if(a__zero(mark(mark(x0))), s(0), prod(mark(x0), fact(p(mark(x0))))), mark(x1)), MARK(fact(x0))) A__ADD(s(fact(fact(z0))), x1) -> c3(A__ADD(a__fact(a__fact(mark(z0))), mark(x1)), MARK(fact(fact(z0)))) A__ADD(s(fact(if(z0, z1, z2))), x1) -> c3(A__ADD(a__fact(a__if(mark(z0), z1, z2)), mark(x1)), MARK(fact(if(z0, z1, z2)))) A__ADD(s(fact(zero(z0))), x1) -> c3(A__ADD(a__fact(a__zero(mark(z0))), mark(x1)), MARK(fact(zero(z0)))) A__ADD(s(fact(prod(z0, z1))), x1) -> c3(A__ADD(a__fact(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(fact(prod(z0, z1)))) A__ADD(s(fact(p(z0))), x1) -> c3(A__ADD(a__fact(a__p(mark(z0))), mark(x1)), MARK(fact(p(z0)))) A__ADD(s(fact(add(z0, z1))), x1) -> c3(A__ADD(a__fact(a__add(mark(z0), mark(z1))), mark(x1)), MARK(fact(add(z0, z1)))) A__ADD(s(fact(s(z0))), x1) -> c3(A__ADD(a__fact(s(mark(z0))), mark(x1)), MARK(fact(s(z0)))) A__ADD(s(fact(0)), x1) -> c3(A__ADD(a__fact(0), mark(x1)), MARK(fact(0))) A__ADD(s(fact(true)), x1) -> c3(A__ADD(a__fact(true), mark(x1)), MARK(fact(true))) A__ADD(s(fact(false)), x1) -> c3(A__ADD(a__fact(false), mark(x1)), MARK(fact(false))) A__ADD(s(fact(x0)), x1) -> c3(MARK(fact(x0))) A__ADD(s(if(x0, z1, z2)), x3) -> c3(A__ADD(if(mark(x0), z1, z2), mark(x3)), MARK(if(x0, z1, z2))) A__ADD(s(if(fact(z0), x1, x2)), x3) -> c3(A__ADD(a__if(a__fact(mark(z0)), x1, x2), mark(x3)), MARK(if(fact(z0), x1, x2))) A__ADD(s(if(if(z0, z1, z2), x1, x2)), x3) -> c3(A__ADD(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(if(if(z0, z1, z2), x1, x2))) A__ADD(s(if(zero(z0), x1, x2)), x3) -> c3(A__ADD(a__if(a__zero(mark(z0)), x1, x2), mark(x3)), MARK(if(zero(z0), x1, x2))) A__ADD(s(if(prod(z0, z1), x1, x2)), x3) -> c3(A__ADD(a__if(a__prod(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(prod(z0, z1), x1, x2))) A__ADD(s(if(p(z0), x1, x2)), x3) -> c3(A__ADD(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(if(p(z0), x1, x2))) A__ADD(s(if(add(z0, z1), x1, x2)), x3) -> c3(A__ADD(a__if(a__add(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(add(z0, z1), x1, x2))) A__ADD(s(if(s(z0), x1, x2)), x3) -> c3(A__ADD(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(if(s(z0), x1, x2))) A__ADD(s(if(0, x1, x2)), x3) -> c3(A__ADD(a__if(0, x1, x2), mark(x3)), MARK(if(0, x1, x2))) A__ADD(s(if(true, x1, x2)), x3) -> c3(A__ADD(a__if(true, x1, x2), mark(x3)), MARK(if(true, x1, x2))) A__ADD(s(if(false, x1, x2)), x3) -> c3(A__ADD(a__if(false, x1, x2), mark(x3)), MARK(if(false, x1, x2))) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__PROD_2, A__FACT_1 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c27_1, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1, c24_2, c25_2, c25_1, c26_2, c26_1, c_2, c_1 ---------------------------------------- (191) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (192) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1)))) A__ADD(s(x0), prod(x1, x2)) -> c3(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), prod(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, p(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, s(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, 0)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), prod(x1, true)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(x0)) A__ADD(s(x0), prod(x1, false)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(x0)) A__ADD(s(x0), prod(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(p(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(0, x2)) -> c3(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(true, x2)) -> c3(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(false, x2)) -> c3(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), prod(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2)))) A__ADD(s(x0), p(x1)) -> c3(A__ADD(mark(x0), p(mark(x1))), MARK(x0)) A__ADD(s(x0), p(fact(z0))) -> c3(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), p(zero(z0))) -> c3(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(p(z0))) -> c3(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(add(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(s(z0))) -> c3(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(0)) -> c3(A__ADD(mark(x0), a__p(0)), MARK(x0)) A__ADD(s(x0), p(true)) -> c3(A__ADD(mark(x0), a__p(true)), MARK(x0)) A__ADD(s(x0), p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1)))) A__ADD(s(x0), add(x1, x2)) -> c3(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), add(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), add(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, p(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, s(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, 0)) -> c3(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), add(x1, true)) -> c3(A__ADD(mark(x0), a__add(mark(x1), true)), MARK(x0)) A__ADD(s(x0), add(x1, false)) -> c3(A__ADD(mark(x0), a__add(mark(x1), false)), MARK(x0)) A__ADD(s(x0), add(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), add(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(p(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(s(z0), x2)) -> c3(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(0, x2)) -> c3(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) A__ADD(s(x0), add(true, x2)) -> c3(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(x0)) A__ADD(s(x0), add(false, x2)) -> c3(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), add(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), add(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), add(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__add(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), add(x1, x2)) -> c3(A__ADD(0, a__add(mark(x1), mark(x2)))) A__ADD(s(x0), s(fact(z0))) -> c3(A__ADD(mark(x0), s(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), s(zero(z0))) -> c3(A__ADD(mark(x0), s(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(prod(z0, z1))) -> c3(A__ADD(mark(x0), s(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(p(z0))) -> c3(A__ADD(mark(x0), s(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(add(z0, z1))) -> c3(A__ADD(mark(x0), s(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(s(z0))) -> c3(A__ADD(mark(x0), s(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(0)) -> c3(A__ADD(mark(x0), s(0)), MARK(x0)) A__ADD(s(x0), s(true)) -> c3(A__ADD(mark(x0), s(true)), MARK(x0)) A__ADD(s(x0), s(false)) -> c3(A__ADD(mark(x0), s(false)), MARK(x0)) A__ADD(s(fact(z0)), s(x1)) -> c3(A__ADD(a__fact(mark(z0)), s(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), s(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), s(x1)) -> c3(A__ADD(a__zero(mark(z0)), s(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), s(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), s(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), s(x1)) -> c3(A__ADD(a__p(mark(z0)), s(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), s(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), s(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), s(x1)) -> c3(A__ADD(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__ADD(s(0), s(x1)) -> c3(A__ADD(0, s(mark(x1)))) A__ADD(s(fact(z0)), 0) -> c3(A__ADD(a__fact(mark(z0)), 0), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), 0) -> c3(A__ADD(a__if(mark(z0), z1, z2), 0), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), 0) -> c3(A__ADD(a__zero(mark(z0)), 0), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), 0) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), 0), MARK(prod(z0, z1))) A__ADD(s(p(z0)), 0) -> c3(A__ADD(a__p(mark(z0)), 0), MARK(p(z0))) A__ADD(s(add(z0, z1)), 0) -> c3(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) A__ADD(s(s(z0)), 0) -> c3(A__ADD(s(mark(z0)), 0), MARK(s(z0))) A__ADD(s(0), 0) -> c3(A__ADD(0, 0)) A__ADD(s(fact(z0)), true) -> c3(A__ADD(a__fact(mark(z0)), true), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), true) -> c3(A__ADD(a__if(mark(z0), z1, z2), true), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), true) -> c3(A__ADD(a__zero(mark(z0)), true), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), true) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), true), MARK(prod(z0, z1))) A__ADD(s(p(z0)), true) -> c3(A__ADD(a__p(mark(z0)), true), MARK(p(z0))) A__ADD(s(add(z0, z1)), true) -> c3(A__ADD(a__add(mark(z0), mark(z1)), true), MARK(add(z0, z1))) A__ADD(s(s(z0)), true) -> c3(A__ADD(s(mark(z0)), true), MARK(s(z0))) A__ADD(s(0), true) -> c3(A__ADD(0, true)) A__ADD(s(fact(z0)), false) -> c3(A__ADD(a__fact(mark(z0)), false), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), false) -> c3(A__ADD(a__if(mark(z0), z1, z2), false), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), false) -> c3(A__ADD(a__zero(mark(z0)), false), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), false) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), false), MARK(prod(z0, z1))) A__ADD(s(p(z0)), false) -> c3(A__ADD(a__p(mark(z0)), false), MARK(p(z0))) A__ADD(s(add(z0, z1)), false) -> c3(A__ADD(a__add(mark(z0), mark(z1)), false), MARK(add(z0, z1))) A__ADD(s(s(z0)), false) -> c3(A__ADD(s(mark(z0)), false), MARK(s(z0))) A__ADD(s(0), false) -> c3(A__ADD(0, false)) A__ADD(s(fact(x0)), x1) -> c3(A__ADD(a__if(a__zero(mark(mark(x0))), s(0), prod(mark(x0), fact(p(mark(x0))))), mark(x1)), MARK(fact(x0))) A__ADD(s(fact(fact(z0))), x1) -> c3(A__ADD(a__fact(a__fact(mark(z0))), mark(x1)), MARK(fact(fact(z0)))) A__ADD(s(fact(if(z0, z1, z2))), x1) -> c3(A__ADD(a__fact(a__if(mark(z0), z1, z2)), mark(x1)), MARK(fact(if(z0, z1, z2)))) A__ADD(s(fact(zero(z0))), x1) -> c3(A__ADD(a__fact(a__zero(mark(z0))), mark(x1)), MARK(fact(zero(z0)))) A__ADD(s(fact(prod(z0, z1))), x1) -> c3(A__ADD(a__fact(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(fact(prod(z0, z1)))) A__ADD(s(fact(p(z0))), x1) -> c3(A__ADD(a__fact(a__p(mark(z0))), mark(x1)), MARK(fact(p(z0)))) A__ADD(s(fact(add(z0, z1))), x1) -> c3(A__ADD(a__fact(a__add(mark(z0), mark(z1))), mark(x1)), MARK(fact(add(z0, z1)))) A__ADD(s(fact(s(z0))), x1) -> c3(A__ADD(a__fact(s(mark(z0))), mark(x1)), MARK(fact(s(z0)))) A__ADD(s(fact(0)), x1) -> c3(A__ADD(a__fact(0), mark(x1)), MARK(fact(0))) A__ADD(s(fact(true)), x1) -> c3(A__ADD(a__fact(true), mark(x1)), MARK(fact(true))) A__ADD(s(fact(false)), x1) -> c3(A__ADD(a__fact(false), mark(x1)), MARK(fact(false))) A__ADD(s(fact(x0)), x1) -> c3(MARK(fact(x0))) A__ADD(s(if(fact(z0), x1, x2)), x3) -> c3(A__ADD(a__if(a__fact(mark(z0)), x1, x2), mark(x3)), MARK(if(fact(z0), x1, x2))) A__ADD(s(if(if(z0, z1, z2), x1, x2)), x3) -> c3(A__ADD(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(if(if(z0, z1, z2), x1, x2))) A__ADD(s(if(zero(z0), x1, x2)), x3) -> c3(A__ADD(a__if(a__zero(mark(z0)), x1, x2), mark(x3)), MARK(if(zero(z0), x1, x2))) A__ADD(s(if(prod(z0, z1), x1, x2)), x3) -> c3(A__ADD(a__if(a__prod(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(prod(z0, z1), x1, x2))) A__ADD(s(if(p(z0), x1, x2)), x3) -> c3(A__ADD(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(if(p(z0), x1, x2))) A__ADD(s(if(add(z0, z1), x1, x2)), x3) -> c3(A__ADD(a__if(a__add(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(add(z0, z1), x1, x2))) A__ADD(s(if(s(z0), x1, x2)), x3) -> c3(A__ADD(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(if(s(z0), x1, x2))) A__ADD(s(if(true, x1, x2)), x3) -> c3(A__ADD(a__if(true, x1, x2), mark(x3)), MARK(if(true, x1, x2))) A__ADD(s(if(false, x1, x2)), x3) -> c3(A__ADD(a__if(false, x1, x2), mark(x3)), MARK(if(false, x1, x2))) A__ADD(s(if(x0, z1, z2)), x3) -> c3(MARK(if(x0, z1, z2))) A__ADD(s(if(0, x1, x2)), x3) -> c3(A__ADD(a__if(0, x1, x2), mark(x3))) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1)))) A__ADD(s(x0), prod(x1, x2)) -> c3(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), prod(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, p(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, s(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, 0)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), prod(x1, true)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(x0)) A__ADD(s(x0), prod(x1, false)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(x0)) A__ADD(s(x0), prod(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(p(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(0, x2)) -> c3(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(true, x2)) -> c3(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(false, x2)) -> c3(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), prod(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2)))) A__ADD(s(x0), p(x1)) -> c3(A__ADD(mark(x0), p(mark(x1))), MARK(x0)) A__ADD(s(x0), p(fact(z0))) -> c3(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), p(zero(z0))) -> c3(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(p(z0))) -> c3(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(add(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(s(z0))) -> c3(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(0)) -> c3(A__ADD(mark(x0), a__p(0)), MARK(x0)) A__ADD(s(x0), p(true)) -> c3(A__ADD(mark(x0), a__p(true)), MARK(x0)) A__ADD(s(x0), p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1)))) A__ADD(s(x0), add(x1, x2)) -> c3(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), add(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), add(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, p(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, s(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, 0)) -> c3(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), add(x1, true)) -> c3(A__ADD(mark(x0), a__add(mark(x1), true)), MARK(x0)) A__ADD(s(x0), add(x1, false)) -> c3(A__ADD(mark(x0), a__add(mark(x1), false)), MARK(x0)) A__ADD(s(x0), add(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), add(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(p(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(s(z0), x2)) -> c3(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(0, x2)) -> c3(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) A__ADD(s(x0), add(true, x2)) -> c3(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(x0)) A__ADD(s(x0), add(false, x2)) -> c3(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), add(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), add(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), add(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__add(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), add(x1, x2)) -> c3(A__ADD(0, a__add(mark(x1), mark(x2)))) A__ADD(s(x0), s(fact(z0))) -> c3(A__ADD(mark(x0), s(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), s(zero(z0))) -> c3(A__ADD(mark(x0), s(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(prod(z0, z1))) -> c3(A__ADD(mark(x0), s(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(p(z0))) -> c3(A__ADD(mark(x0), s(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(add(z0, z1))) -> c3(A__ADD(mark(x0), s(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(s(z0))) -> c3(A__ADD(mark(x0), s(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(0)) -> c3(A__ADD(mark(x0), s(0)), MARK(x0)) A__ADD(s(x0), s(true)) -> c3(A__ADD(mark(x0), s(true)), MARK(x0)) A__ADD(s(x0), s(false)) -> c3(A__ADD(mark(x0), s(false)), MARK(x0)) A__ADD(s(fact(z0)), s(x1)) -> c3(A__ADD(a__fact(mark(z0)), s(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), s(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), s(x1)) -> c3(A__ADD(a__zero(mark(z0)), s(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), s(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), s(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), s(x1)) -> c3(A__ADD(a__p(mark(z0)), s(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), s(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), s(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), s(x1)) -> c3(A__ADD(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__ADD(s(0), s(x1)) -> c3(A__ADD(0, s(mark(x1)))) A__ADD(s(fact(z0)), 0) -> c3(A__ADD(a__fact(mark(z0)), 0), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), 0) -> c3(A__ADD(a__if(mark(z0), z1, z2), 0), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), 0) -> c3(A__ADD(a__zero(mark(z0)), 0), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), 0) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), 0), MARK(prod(z0, z1))) A__ADD(s(p(z0)), 0) -> c3(A__ADD(a__p(mark(z0)), 0), MARK(p(z0))) A__ADD(s(add(z0, z1)), 0) -> c3(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) A__ADD(s(s(z0)), 0) -> c3(A__ADD(s(mark(z0)), 0), MARK(s(z0))) A__ADD(s(0), 0) -> c3(A__ADD(0, 0)) A__ADD(s(fact(z0)), true) -> c3(A__ADD(a__fact(mark(z0)), true), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), true) -> c3(A__ADD(a__if(mark(z0), z1, z2), true), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), true) -> c3(A__ADD(a__zero(mark(z0)), true), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), true) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), true), MARK(prod(z0, z1))) A__ADD(s(p(z0)), true) -> c3(A__ADD(a__p(mark(z0)), true), MARK(p(z0))) A__ADD(s(add(z0, z1)), true) -> c3(A__ADD(a__add(mark(z0), mark(z1)), true), MARK(add(z0, z1))) A__ADD(s(s(z0)), true) -> c3(A__ADD(s(mark(z0)), true), MARK(s(z0))) A__ADD(s(0), true) -> c3(A__ADD(0, true)) A__ADD(s(fact(z0)), false) -> c3(A__ADD(a__fact(mark(z0)), false), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), false) -> c3(A__ADD(a__if(mark(z0), z1, z2), false), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), false) -> c3(A__ADD(a__zero(mark(z0)), false), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), false) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), false), MARK(prod(z0, z1))) A__ADD(s(p(z0)), false) -> c3(A__ADD(a__p(mark(z0)), false), MARK(p(z0))) A__ADD(s(add(z0, z1)), false) -> c3(A__ADD(a__add(mark(z0), mark(z1)), false), MARK(add(z0, z1))) A__ADD(s(s(z0)), false) -> c3(A__ADD(s(mark(z0)), false), MARK(s(z0))) A__ADD(s(0), false) -> c3(A__ADD(0, false)) A__ADD(s(fact(x0)), x1) -> c3(A__ADD(a__if(a__zero(mark(mark(x0))), s(0), prod(mark(x0), fact(p(mark(x0))))), mark(x1)), MARK(fact(x0))) A__ADD(s(fact(fact(z0))), x1) -> c3(A__ADD(a__fact(a__fact(mark(z0))), mark(x1)), MARK(fact(fact(z0)))) A__ADD(s(fact(if(z0, z1, z2))), x1) -> c3(A__ADD(a__fact(a__if(mark(z0), z1, z2)), mark(x1)), MARK(fact(if(z0, z1, z2)))) A__ADD(s(fact(zero(z0))), x1) -> c3(A__ADD(a__fact(a__zero(mark(z0))), mark(x1)), MARK(fact(zero(z0)))) A__ADD(s(fact(prod(z0, z1))), x1) -> c3(A__ADD(a__fact(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(fact(prod(z0, z1)))) A__ADD(s(fact(p(z0))), x1) -> c3(A__ADD(a__fact(a__p(mark(z0))), mark(x1)), MARK(fact(p(z0)))) A__ADD(s(fact(add(z0, z1))), x1) -> c3(A__ADD(a__fact(a__add(mark(z0), mark(z1))), mark(x1)), MARK(fact(add(z0, z1)))) A__ADD(s(fact(s(z0))), x1) -> c3(A__ADD(a__fact(s(mark(z0))), mark(x1)), MARK(fact(s(z0)))) A__ADD(s(fact(0)), x1) -> c3(A__ADD(a__fact(0), mark(x1)), MARK(fact(0))) A__ADD(s(fact(true)), x1) -> c3(A__ADD(a__fact(true), mark(x1)), MARK(fact(true))) A__ADD(s(fact(false)), x1) -> c3(A__ADD(a__fact(false), mark(x1)), MARK(fact(false))) A__ADD(s(fact(x0)), x1) -> c3(MARK(fact(x0))) A__ADD(s(if(fact(z0), x1, x2)), x3) -> c3(A__ADD(a__if(a__fact(mark(z0)), x1, x2), mark(x3)), MARK(if(fact(z0), x1, x2))) A__ADD(s(if(if(z0, z1, z2), x1, x2)), x3) -> c3(A__ADD(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(if(if(z0, z1, z2), x1, x2))) A__ADD(s(if(zero(z0), x1, x2)), x3) -> c3(A__ADD(a__if(a__zero(mark(z0)), x1, x2), mark(x3)), MARK(if(zero(z0), x1, x2))) A__ADD(s(if(prod(z0, z1), x1, x2)), x3) -> c3(A__ADD(a__if(a__prod(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(prod(z0, z1), x1, x2))) A__ADD(s(if(p(z0), x1, x2)), x3) -> c3(A__ADD(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(if(p(z0), x1, x2))) A__ADD(s(if(add(z0, z1), x1, x2)), x3) -> c3(A__ADD(a__if(a__add(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(add(z0, z1), x1, x2))) A__ADD(s(if(s(z0), x1, x2)), x3) -> c3(A__ADD(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(if(s(z0), x1, x2))) A__ADD(s(if(true, x1, x2)), x3) -> c3(A__ADD(a__if(true, x1, x2), mark(x3)), MARK(if(true, x1, x2))) A__ADD(s(if(false, x1, x2)), x3) -> c3(A__ADD(a__if(false, x1, x2), mark(x3)), MARK(if(false, x1, x2))) A__ADD(s(if(x0, z1, z2)), x3) -> c3(MARK(if(x0, z1, z2))) A__ADD(s(if(0, x1, x2)), x3) -> c3(A__ADD(a__if(0, x1, x2), mark(x3))) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__PROD_2, A__FACT_1 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c27_1, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1, c24_2, c25_2, c25_1, c26_2, c26_1, c_2, c_1 ---------------------------------------- (193) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__ADD(s(zero(z0)), x1) -> c3(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) by A__ADD(s(zero(x0)), fact(z0)) -> c3(A__ADD(a__zero(mark(x0)), a__fact(mark(z0))), MARK(zero(x0))) A__ADD(s(zero(x0)), if(z0, z1, z2)) -> c3(A__ADD(a__zero(mark(x0)), a__if(mark(z0), z1, z2)), MARK(zero(x0))) A__ADD(s(zero(x0)), zero(z0)) -> c3(A__ADD(a__zero(mark(x0)), a__zero(mark(z0))), MARK(zero(x0))) A__ADD(s(zero(x0)), prod(z0, z1)) -> c3(A__ADD(a__zero(mark(x0)), a__prod(mark(z0), mark(z1))), MARK(zero(x0))) A__ADD(s(zero(x0)), p(z0)) -> c3(A__ADD(a__zero(mark(x0)), a__p(mark(z0))), MARK(zero(x0))) A__ADD(s(zero(x0)), add(z0, z1)) -> c3(A__ADD(a__zero(mark(x0)), a__add(mark(z0), mark(z1))), MARK(zero(x0))) A__ADD(s(zero(x0)), s(z0)) -> c3(A__ADD(a__zero(mark(x0)), s(mark(z0))), MARK(zero(x0))) A__ADD(s(zero(x0)), 0) -> c3(A__ADD(a__zero(mark(x0)), 0), MARK(zero(x0))) A__ADD(s(zero(x0)), true) -> c3(A__ADD(a__zero(mark(x0)), true), MARK(zero(x0))) A__ADD(s(zero(x0)), false) -> c3(A__ADD(a__zero(mark(x0)), false), MARK(zero(x0))) A__ADD(s(zero(x0)), x1) -> c3(A__ADD(zero(mark(x0)), mark(x1)), MARK(zero(x0))) A__ADD(s(zero(fact(z0))), x1) -> c3(A__ADD(a__zero(a__fact(mark(z0))), mark(x1)), MARK(zero(fact(z0)))) A__ADD(s(zero(if(z0, z1, z2))), x1) -> c3(A__ADD(a__zero(a__if(mark(z0), z1, z2)), mark(x1)), MARK(zero(if(z0, z1, z2)))) A__ADD(s(zero(zero(z0))), x1) -> c3(A__ADD(a__zero(a__zero(mark(z0))), mark(x1)), MARK(zero(zero(z0)))) A__ADD(s(zero(prod(z0, z1))), x1) -> c3(A__ADD(a__zero(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(zero(prod(z0, z1)))) A__ADD(s(zero(p(z0))), x1) -> c3(A__ADD(a__zero(a__p(mark(z0))), mark(x1)), MARK(zero(p(z0)))) A__ADD(s(zero(add(z0, z1))), x1) -> c3(A__ADD(a__zero(a__add(mark(z0), mark(z1))), mark(x1)), MARK(zero(add(z0, z1)))) A__ADD(s(zero(s(z0))), x1) -> c3(A__ADD(a__zero(s(mark(z0))), mark(x1)), MARK(zero(s(z0)))) A__ADD(s(zero(0)), x1) -> c3(A__ADD(a__zero(0), mark(x1)), MARK(zero(0))) A__ADD(s(zero(true)), x1) -> c3(A__ADD(a__zero(true), mark(x1)), MARK(zero(true))) A__ADD(s(zero(false)), x1) -> c3(A__ADD(a__zero(false), mark(x1)), MARK(zero(false))) A__ADD(s(zero(x0)), x1) -> c3(MARK(zero(x0))) ---------------------------------------- (194) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, 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a__p(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(add(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(s(z0))) -> c3(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(0)) -> c3(A__ADD(mark(x0), a__p(0)), MARK(x0)) A__ADD(s(x0), p(true)) -> c3(A__ADD(mark(x0), a__p(true)), MARK(x0)) A__ADD(s(x0), p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1)))) A__ADD(s(x0), add(x1, x2)) -> c3(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), add(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), add(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, p(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, s(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, 0)) -> c3(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), add(x1, true)) -> c3(A__ADD(mark(x0), a__add(mark(x1), true)), MARK(x0)) A__ADD(s(x0), add(x1, false)) -> c3(A__ADD(mark(x0), a__add(mark(x1), false)), MARK(x0)) A__ADD(s(x0), add(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), add(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(p(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(s(z0), x2)) -> c3(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(0, x2)) -> c3(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) A__ADD(s(x0), add(true, x2)) -> c3(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(x0)) A__ADD(s(x0), add(false, x2)) -> c3(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), add(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), add(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), add(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__add(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), add(x1, x2)) -> c3(A__ADD(0, a__add(mark(x1), mark(x2)))) A__ADD(s(x0), s(fact(z0))) -> c3(A__ADD(mark(x0), s(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), s(zero(z0))) -> c3(A__ADD(mark(x0), s(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(prod(z0, z1))) -> c3(A__ADD(mark(x0), s(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(p(z0))) -> c3(A__ADD(mark(x0), s(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(add(z0, z1))) -> c3(A__ADD(mark(x0), s(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(s(z0))) -> c3(A__ADD(mark(x0), s(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(0)) -> c3(A__ADD(mark(x0), s(0)), MARK(x0)) A__ADD(s(x0), s(true)) -> c3(A__ADD(mark(x0), s(true)), MARK(x0)) A__ADD(s(x0), s(false)) -> c3(A__ADD(mark(x0), s(false)), MARK(x0)) A__ADD(s(fact(z0)), s(x1)) -> c3(A__ADD(a__fact(mark(z0)), s(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), s(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), s(x1)) -> c3(A__ADD(a__zero(mark(z0)), s(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), s(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), s(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), s(x1)) -> c3(A__ADD(a__p(mark(z0)), s(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), s(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), s(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), s(x1)) -> c3(A__ADD(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__ADD(s(0), s(x1)) -> c3(A__ADD(0, s(mark(x1)))) A__ADD(s(fact(z0)), 0) -> c3(A__ADD(a__fact(mark(z0)), 0), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), 0) -> c3(A__ADD(a__if(mark(z0), z1, z2), 0), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), 0) -> c3(A__ADD(a__zero(mark(z0)), 0), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), 0) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), 0), MARK(prod(z0, z1))) A__ADD(s(p(z0)), 0) -> c3(A__ADD(a__p(mark(z0)), 0), MARK(p(z0))) A__ADD(s(add(z0, z1)), 0) -> c3(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) A__ADD(s(s(z0)), 0) -> c3(A__ADD(s(mark(z0)), 0), MARK(s(z0))) A__ADD(s(0), 0) -> c3(A__ADD(0, 0)) A__ADD(s(fact(z0)), true) -> c3(A__ADD(a__fact(mark(z0)), true), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), true) -> c3(A__ADD(a__if(mark(z0), z1, z2), true), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), true) -> c3(A__ADD(a__zero(mark(z0)), true), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), true) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), true), MARK(prod(z0, z1))) A__ADD(s(p(z0)), true) -> c3(A__ADD(a__p(mark(z0)), true), MARK(p(z0))) A__ADD(s(add(z0, z1)), true) -> c3(A__ADD(a__add(mark(z0), mark(z1)), true), MARK(add(z0, z1))) A__ADD(s(s(z0)), true) -> c3(A__ADD(s(mark(z0)), true), MARK(s(z0))) A__ADD(s(0), true) -> c3(A__ADD(0, true)) A__ADD(s(fact(z0)), false) -> c3(A__ADD(a__fact(mark(z0)), false), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), false) -> c3(A__ADD(a__if(mark(z0), z1, z2), false), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), false) -> c3(A__ADD(a__zero(mark(z0)), false), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), false) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), false), MARK(prod(z0, z1))) A__ADD(s(p(z0)), false) -> c3(A__ADD(a__p(mark(z0)), false), MARK(p(z0))) A__ADD(s(add(z0, z1)), false) -> c3(A__ADD(a__add(mark(z0), mark(z1)), false), MARK(add(z0, z1))) A__ADD(s(s(z0)), false) -> c3(A__ADD(s(mark(z0)), false), MARK(s(z0))) A__ADD(s(0), false) -> c3(A__ADD(0, false)) A__ADD(s(fact(x0)), x1) -> c3(A__ADD(a__if(a__zero(mark(mark(x0))), s(0), prod(mark(x0), fact(p(mark(x0))))), mark(x1)), MARK(fact(x0))) A__ADD(s(fact(fact(z0))), x1) -> c3(A__ADD(a__fact(a__fact(mark(z0))), mark(x1)), MARK(fact(fact(z0)))) A__ADD(s(fact(if(z0, z1, z2))), x1) -> c3(A__ADD(a__fact(a__if(mark(z0), z1, z2)), mark(x1)), MARK(fact(if(z0, z1, z2)))) A__ADD(s(fact(zero(z0))), x1) -> c3(A__ADD(a__fact(a__zero(mark(z0))), mark(x1)), MARK(fact(zero(z0)))) A__ADD(s(fact(prod(z0, z1))), x1) -> c3(A__ADD(a__fact(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(fact(prod(z0, z1)))) A__ADD(s(fact(p(z0))), x1) -> c3(A__ADD(a__fact(a__p(mark(z0))), mark(x1)), MARK(fact(p(z0)))) A__ADD(s(fact(add(z0, z1))), x1) -> c3(A__ADD(a__fact(a__add(mark(z0), mark(z1))), mark(x1)), MARK(fact(add(z0, z1)))) A__ADD(s(fact(s(z0))), x1) -> c3(A__ADD(a__fact(s(mark(z0))), mark(x1)), MARK(fact(s(z0)))) A__ADD(s(fact(0)), x1) -> c3(A__ADD(a__fact(0), mark(x1)), MARK(fact(0))) A__ADD(s(fact(true)), x1) -> c3(A__ADD(a__fact(true), mark(x1)), MARK(fact(true))) A__ADD(s(fact(false)), x1) -> c3(A__ADD(a__fact(false), mark(x1)), MARK(fact(false))) A__ADD(s(fact(x0)), x1) -> c3(MARK(fact(x0))) A__ADD(s(if(fact(z0), x1, x2)), x3) -> c3(A__ADD(a__if(a__fact(mark(z0)), x1, x2), mark(x3)), MARK(if(fact(z0), x1, x2))) A__ADD(s(if(if(z0, z1, z2), x1, x2)), x3) -> c3(A__ADD(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(if(if(z0, z1, z2), x1, x2))) A__ADD(s(if(zero(z0), x1, x2)), x3) -> c3(A__ADD(a__if(a__zero(mark(z0)), x1, x2), mark(x3)), MARK(if(zero(z0), x1, x2))) A__ADD(s(if(prod(z0, z1), x1, x2)), x3) -> c3(A__ADD(a__if(a__prod(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(prod(z0, z1), x1, x2))) A__ADD(s(if(p(z0), x1, x2)), x3) -> c3(A__ADD(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(if(p(z0), x1, x2))) A__ADD(s(if(add(z0, z1), x1, x2)), x3) -> c3(A__ADD(a__if(a__add(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(add(z0, z1), x1, x2))) A__ADD(s(if(s(z0), x1, x2)), x3) -> c3(A__ADD(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(if(s(z0), x1, x2))) A__ADD(s(if(true, x1, x2)), x3) -> c3(A__ADD(a__if(true, x1, x2), mark(x3)), MARK(if(true, x1, x2))) A__ADD(s(if(false, x1, x2)), x3) -> c3(A__ADD(a__if(false, x1, x2), mark(x3)), MARK(if(false, x1, x2))) A__ADD(s(if(x0, z1, z2)), x3) -> c3(MARK(if(x0, z1, z2))) A__ADD(s(if(0, x1, x2)), x3) -> c3(A__ADD(a__if(0, x1, x2), mark(x3))) A__ADD(s(zero(x0)), x1) -> c3(A__ADD(zero(mark(x0)), mark(x1)), MARK(zero(x0))) A__ADD(s(zero(fact(z0))), x1) -> c3(A__ADD(a__zero(a__fact(mark(z0))), mark(x1)), MARK(zero(fact(z0)))) A__ADD(s(zero(if(z0, z1, z2))), x1) -> c3(A__ADD(a__zero(a__if(mark(z0), z1, z2)), mark(x1)), MARK(zero(if(z0, z1, z2)))) A__ADD(s(zero(zero(z0))), x1) -> c3(A__ADD(a__zero(a__zero(mark(z0))), mark(x1)), MARK(zero(zero(z0)))) A__ADD(s(zero(prod(z0, z1))), x1) -> c3(A__ADD(a__zero(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(zero(prod(z0, z1)))) A__ADD(s(zero(p(z0))), x1) -> c3(A__ADD(a__zero(a__p(mark(z0))), mark(x1)), MARK(zero(p(z0)))) A__ADD(s(zero(add(z0, z1))), x1) -> c3(A__ADD(a__zero(a__add(mark(z0), mark(z1))), mark(x1)), MARK(zero(add(z0, z1)))) A__ADD(s(zero(s(z0))), x1) -> c3(A__ADD(a__zero(s(mark(z0))), mark(x1)), MARK(zero(s(z0)))) A__ADD(s(zero(0)), x1) -> c3(A__ADD(a__zero(0), mark(x1)), MARK(zero(0))) A__ADD(s(zero(true)), x1) -> c3(A__ADD(a__zero(true), mark(x1)), MARK(zero(true))) A__ADD(s(zero(false)), x1) -> c3(A__ADD(a__zero(false), mark(x1)), MARK(zero(false))) A__ADD(s(zero(x0)), x1) -> c3(MARK(zero(x0))) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), 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A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), prod(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, p(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, s(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, 0)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), prod(x1, true)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(x0)) A__ADD(s(x0), prod(x1, false)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(x0)) A__ADD(s(x0), prod(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(p(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(0, x2)) -> c3(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(true, x2)) -> c3(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(false, x2)) -> c3(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), prod(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2)))) A__ADD(s(x0), p(x1)) -> c3(A__ADD(mark(x0), p(mark(x1))), MARK(x0)) A__ADD(s(x0), p(fact(z0))) -> c3(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), p(zero(z0))) -> c3(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(p(z0))) -> c3(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(add(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(s(z0))) -> c3(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(0)) -> c3(A__ADD(mark(x0), a__p(0)), MARK(x0)) A__ADD(s(x0), p(true)) -> c3(A__ADD(mark(x0), a__p(true)), MARK(x0)) A__ADD(s(x0), p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1)))) A__ADD(s(x0), add(x1, x2)) -> c3(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), add(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), add(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, p(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, s(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, 0)) -> c3(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), add(x1, true)) -> c3(A__ADD(mark(x0), a__add(mark(x1), true)), MARK(x0)) A__ADD(s(x0), add(x1, false)) -> c3(A__ADD(mark(x0), a__add(mark(x1), false)), MARK(x0)) A__ADD(s(x0), add(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), add(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(p(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(s(z0), x2)) -> c3(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(0, x2)) -> c3(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) A__ADD(s(x0), add(true, x2)) -> c3(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(x0)) A__ADD(s(x0), add(false, x2)) -> c3(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), add(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), add(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), add(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__add(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), add(x1, x2)) -> c3(A__ADD(0, a__add(mark(x1), mark(x2)))) A__ADD(s(x0), s(fact(z0))) -> c3(A__ADD(mark(x0), s(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), s(zero(z0))) -> c3(A__ADD(mark(x0), s(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(prod(z0, z1))) -> c3(A__ADD(mark(x0), s(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(p(z0))) -> c3(A__ADD(mark(x0), s(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(add(z0, z1))) -> c3(A__ADD(mark(x0), s(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(s(z0))) -> c3(A__ADD(mark(x0), s(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(0)) -> c3(A__ADD(mark(x0), s(0)), MARK(x0)) A__ADD(s(x0), s(true)) -> c3(A__ADD(mark(x0), s(true)), MARK(x0)) A__ADD(s(x0), s(false)) -> c3(A__ADD(mark(x0), s(false)), MARK(x0)) A__ADD(s(fact(z0)), s(x1)) -> c3(A__ADD(a__fact(mark(z0)), s(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), s(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), s(x1)) -> c3(A__ADD(a__zero(mark(z0)), s(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), s(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), s(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), s(x1)) -> c3(A__ADD(a__p(mark(z0)), s(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), s(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), s(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), s(x1)) -> c3(A__ADD(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__ADD(s(0), s(x1)) -> c3(A__ADD(0, s(mark(x1)))) A__ADD(s(fact(z0)), 0) -> c3(A__ADD(a__fact(mark(z0)), 0), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), 0) -> c3(A__ADD(a__if(mark(z0), z1, z2), 0), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), 0) -> c3(A__ADD(a__zero(mark(z0)), 0), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), 0) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), 0), MARK(prod(z0, z1))) A__ADD(s(p(z0)), 0) -> c3(A__ADD(a__p(mark(z0)), 0), MARK(p(z0))) A__ADD(s(add(z0, z1)), 0) -> c3(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) A__ADD(s(s(z0)), 0) -> c3(A__ADD(s(mark(z0)), 0), MARK(s(z0))) A__ADD(s(0), 0) -> c3(A__ADD(0, 0)) A__ADD(s(fact(z0)), true) -> c3(A__ADD(a__fact(mark(z0)), true), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), true) -> c3(A__ADD(a__if(mark(z0), z1, z2), true), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), true) -> c3(A__ADD(a__zero(mark(z0)), true), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), true) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), true), MARK(prod(z0, z1))) A__ADD(s(p(z0)), true) -> c3(A__ADD(a__p(mark(z0)), true), MARK(p(z0))) A__ADD(s(add(z0, z1)), true) -> c3(A__ADD(a__add(mark(z0), mark(z1)), true), MARK(add(z0, z1))) A__ADD(s(s(z0)), true) -> c3(A__ADD(s(mark(z0)), true), MARK(s(z0))) A__ADD(s(0), true) -> c3(A__ADD(0, true)) A__ADD(s(fact(z0)), false) -> c3(A__ADD(a__fact(mark(z0)), false), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), false) -> c3(A__ADD(a__if(mark(z0), z1, z2), false), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), false) -> c3(A__ADD(a__zero(mark(z0)), false), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), false) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), false), MARK(prod(z0, z1))) A__ADD(s(p(z0)), false) -> c3(A__ADD(a__p(mark(z0)), false), MARK(p(z0))) A__ADD(s(add(z0, z1)), false) -> c3(A__ADD(a__add(mark(z0), mark(z1)), false), MARK(add(z0, z1))) A__ADD(s(s(z0)), false) -> c3(A__ADD(s(mark(z0)), false), MARK(s(z0))) A__ADD(s(0), false) -> c3(A__ADD(0, false)) A__ADD(s(fact(x0)), x1) -> c3(A__ADD(a__if(a__zero(mark(mark(x0))), s(0), prod(mark(x0), fact(p(mark(x0))))), mark(x1)), MARK(fact(x0))) A__ADD(s(fact(fact(z0))), x1) -> c3(A__ADD(a__fact(a__fact(mark(z0))), mark(x1)), MARK(fact(fact(z0)))) A__ADD(s(fact(if(z0, z1, z2))), x1) -> c3(A__ADD(a__fact(a__if(mark(z0), z1, z2)), mark(x1)), MARK(fact(if(z0, z1, z2)))) A__ADD(s(fact(zero(z0))), x1) -> c3(A__ADD(a__fact(a__zero(mark(z0))), mark(x1)), MARK(fact(zero(z0)))) A__ADD(s(fact(prod(z0, z1))), x1) -> c3(A__ADD(a__fact(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(fact(prod(z0, z1)))) A__ADD(s(fact(p(z0))), x1) -> c3(A__ADD(a__fact(a__p(mark(z0))), mark(x1)), MARK(fact(p(z0)))) A__ADD(s(fact(add(z0, z1))), x1) -> c3(A__ADD(a__fact(a__add(mark(z0), mark(z1))), mark(x1)), MARK(fact(add(z0, z1)))) A__ADD(s(fact(s(z0))), x1) -> c3(A__ADD(a__fact(s(mark(z0))), mark(x1)), MARK(fact(s(z0)))) A__ADD(s(fact(0)), x1) -> c3(A__ADD(a__fact(0), mark(x1)), MARK(fact(0))) A__ADD(s(fact(true)), x1) -> c3(A__ADD(a__fact(true), mark(x1)), MARK(fact(true))) A__ADD(s(fact(false)), x1) -> c3(A__ADD(a__fact(false), mark(x1)), MARK(fact(false))) A__ADD(s(fact(x0)), x1) -> c3(MARK(fact(x0))) A__ADD(s(if(fact(z0), x1, x2)), x3) -> c3(A__ADD(a__if(a__fact(mark(z0)), x1, x2), mark(x3)), MARK(if(fact(z0), x1, x2))) A__ADD(s(if(if(z0, z1, z2), x1, x2)), x3) -> c3(A__ADD(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(if(if(z0, z1, z2), x1, x2))) A__ADD(s(if(zero(z0), x1, x2)), x3) -> c3(A__ADD(a__if(a__zero(mark(z0)), x1, x2), mark(x3)), MARK(if(zero(z0), x1, x2))) A__ADD(s(if(prod(z0, z1), x1, x2)), x3) -> c3(A__ADD(a__if(a__prod(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(prod(z0, z1), x1, x2))) A__ADD(s(if(p(z0), x1, x2)), x3) -> c3(A__ADD(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(if(p(z0), x1, x2))) A__ADD(s(if(add(z0, z1), x1, x2)), x3) -> c3(A__ADD(a__if(a__add(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(add(z0, z1), x1, x2))) A__ADD(s(if(s(z0), x1, x2)), x3) -> c3(A__ADD(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(if(s(z0), x1, x2))) A__ADD(s(if(true, x1, x2)), x3) -> c3(A__ADD(a__if(true, x1, x2), mark(x3)), MARK(if(true, x1, x2))) A__ADD(s(if(false, x1, x2)), x3) -> c3(A__ADD(a__if(false, x1, x2), mark(x3)), MARK(if(false, x1, x2))) A__ADD(s(if(x0, z1, z2)), x3) -> c3(MARK(if(x0, z1, z2))) A__ADD(s(if(0, x1, x2)), x3) -> c3(A__ADD(a__if(0, x1, x2), mark(x3))) A__ADD(s(zero(x0)), x1) -> c3(A__ADD(zero(mark(x0)), mark(x1)), MARK(zero(x0))) A__ADD(s(zero(fact(z0))), x1) -> c3(A__ADD(a__zero(a__fact(mark(z0))), mark(x1)), MARK(zero(fact(z0)))) A__ADD(s(zero(if(z0, z1, z2))), x1) -> c3(A__ADD(a__zero(a__if(mark(z0), z1, z2)), mark(x1)), MARK(zero(if(z0, z1, z2)))) A__ADD(s(zero(zero(z0))), x1) -> c3(A__ADD(a__zero(a__zero(mark(z0))), mark(x1)), MARK(zero(zero(z0)))) A__ADD(s(zero(prod(z0, z1))), x1) -> c3(A__ADD(a__zero(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(zero(prod(z0, z1)))) A__ADD(s(zero(p(z0))), x1) -> c3(A__ADD(a__zero(a__p(mark(z0))), mark(x1)), MARK(zero(p(z0)))) A__ADD(s(zero(add(z0, z1))), x1) -> c3(A__ADD(a__zero(a__add(mark(z0), mark(z1))), mark(x1)), MARK(zero(add(z0, z1)))) A__ADD(s(zero(s(z0))), x1) -> c3(A__ADD(a__zero(s(mark(z0))), mark(x1)), MARK(zero(s(z0)))) A__ADD(s(zero(0)), x1) -> c3(A__ADD(a__zero(0), mark(x1)), MARK(zero(0))) A__ADD(s(zero(true)), x1) -> c3(A__ADD(a__zero(true), mark(x1)), MARK(zero(true))) A__ADD(s(zero(false)), x1) -> c3(A__ADD(a__zero(false), mark(x1)), MARK(zero(false))) A__ADD(s(zero(x0)), x1) -> c3(MARK(zero(x0))) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__PROD_2, A__FACT_1 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c27_1, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1, c24_2, c25_2, c25_1, c26_2, c26_1, c_2, c_1 ---------------------------------------- (195) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (196) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> 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c3(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(p(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(0, x2)) -> c3(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(true, x2)) -> c3(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(false, x2)) -> c3(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), prod(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2)))) A__ADD(s(x0), p(x1)) -> c3(A__ADD(mark(x0), p(mark(x1))), MARK(x0)) A__ADD(s(x0), p(fact(z0))) -> c3(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), p(zero(z0))) -> c3(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(p(z0))) -> c3(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(add(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(s(z0))) -> c3(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(0)) -> c3(A__ADD(mark(x0), a__p(0)), MARK(x0)) A__ADD(s(x0), p(true)) -> c3(A__ADD(mark(x0), a__p(true)), MARK(x0)) A__ADD(s(x0), p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1)))) A__ADD(s(x0), add(x1, x2)) -> c3(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), add(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), add(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, p(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, s(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, 0)) -> c3(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), add(x1, true)) -> c3(A__ADD(mark(x0), a__add(mark(x1), true)), MARK(x0)) A__ADD(s(x0), add(x1, false)) -> c3(A__ADD(mark(x0), a__add(mark(x1), false)), MARK(x0)) A__ADD(s(x0), add(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), add(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(p(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(s(z0), x2)) -> c3(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(0, x2)) -> c3(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) A__ADD(s(x0), add(true, x2)) -> c3(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(x0)) A__ADD(s(x0), add(false, x2)) -> c3(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), add(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), add(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), add(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__add(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), add(x1, x2)) -> c3(A__ADD(0, a__add(mark(x1), mark(x2)))) A__ADD(s(x0), s(fact(z0))) -> c3(A__ADD(mark(x0), s(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), s(zero(z0))) -> c3(A__ADD(mark(x0), s(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(prod(z0, z1))) -> c3(A__ADD(mark(x0), s(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(p(z0))) -> c3(A__ADD(mark(x0), s(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(add(z0, z1))) -> c3(A__ADD(mark(x0), s(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(s(z0))) -> c3(A__ADD(mark(x0), s(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(0)) -> c3(A__ADD(mark(x0), s(0)), MARK(x0)) A__ADD(s(x0), s(true)) -> c3(A__ADD(mark(x0), s(true)), MARK(x0)) A__ADD(s(x0), s(false)) -> c3(A__ADD(mark(x0), s(false)), MARK(x0)) A__ADD(s(fact(z0)), s(x1)) -> c3(A__ADD(a__fact(mark(z0)), s(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), s(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), s(x1)) -> c3(A__ADD(a__zero(mark(z0)), s(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), s(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), s(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), s(x1)) -> c3(A__ADD(a__p(mark(z0)), s(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), s(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), s(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), s(x1)) -> c3(A__ADD(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__ADD(s(0), s(x1)) -> c3(A__ADD(0, s(mark(x1)))) A__ADD(s(fact(z0)), 0) -> c3(A__ADD(a__fact(mark(z0)), 0), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), 0) -> c3(A__ADD(a__if(mark(z0), z1, z2), 0), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), 0) -> c3(A__ADD(a__zero(mark(z0)), 0), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), 0) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), 0), MARK(prod(z0, z1))) A__ADD(s(p(z0)), 0) -> c3(A__ADD(a__p(mark(z0)), 0), MARK(p(z0))) A__ADD(s(add(z0, z1)), 0) -> c3(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) A__ADD(s(s(z0)), 0) -> c3(A__ADD(s(mark(z0)), 0), MARK(s(z0))) A__ADD(s(0), 0) -> c3(A__ADD(0, 0)) A__ADD(s(fact(z0)), true) -> c3(A__ADD(a__fact(mark(z0)), true), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), true) -> c3(A__ADD(a__if(mark(z0), z1, z2), true), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), true) -> c3(A__ADD(a__zero(mark(z0)), true), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), true) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), true), MARK(prod(z0, z1))) A__ADD(s(p(z0)), true) -> c3(A__ADD(a__p(mark(z0)), true), MARK(p(z0))) A__ADD(s(add(z0, z1)), true) -> c3(A__ADD(a__add(mark(z0), mark(z1)), true), MARK(add(z0, z1))) A__ADD(s(s(z0)), true) -> c3(A__ADD(s(mark(z0)), true), MARK(s(z0))) A__ADD(s(0), true) -> c3(A__ADD(0, true)) A__ADD(s(fact(z0)), false) -> c3(A__ADD(a__fact(mark(z0)), false), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), false) -> c3(A__ADD(a__if(mark(z0), z1, z2), false), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), false) -> c3(A__ADD(a__zero(mark(z0)), false), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), false) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), false), MARK(prod(z0, z1))) A__ADD(s(p(z0)), false) -> c3(A__ADD(a__p(mark(z0)), false), MARK(p(z0))) A__ADD(s(add(z0, z1)), false) -> c3(A__ADD(a__add(mark(z0), mark(z1)), false), MARK(add(z0, z1))) A__ADD(s(s(z0)), false) -> c3(A__ADD(s(mark(z0)), false), MARK(s(z0))) A__ADD(s(0), false) -> c3(A__ADD(0, false)) A__ADD(s(fact(x0)), x1) -> c3(A__ADD(a__if(a__zero(mark(mark(x0))), s(0), prod(mark(x0), fact(p(mark(x0))))), mark(x1)), MARK(fact(x0))) A__ADD(s(fact(fact(z0))), x1) -> c3(A__ADD(a__fact(a__fact(mark(z0))), mark(x1)), MARK(fact(fact(z0)))) A__ADD(s(fact(if(z0, z1, z2))), x1) -> c3(A__ADD(a__fact(a__if(mark(z0), z1, z2)), mark(x1)), MARK(fact(if(z0, z1, z2)))) A__ADD(s(fact(zero(z0))), x1) -> c3(A__ADD(a__fact(a__zero(mark(z0))), mark(x1)), MARK(fact(zero(z0)))) A__ADD(s(fact(prod(z0, z1))), x1) -> c3(A__ADD(a__fact(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(fact(prod(z0, z1)))) A__ADD(s(fact(p(z0))), x1) -> c3(A__ADD(a__fact(a__p(mark(z0))), mark(x1)), MARK(fact(p(z0)))) A__ADD(s(fact(add(z0, z1))), x1) -> c3(A__ADD(a__fact(a__add(mark(z0), mark(z1))), mark(x1)), MARK(fact(add(z0, z1)))) A__ADD(s(fact(s(z0))), x1) -> c3(A__ADD(a__fact(s(mark(z0))), mark(x1)), MARK(fact(s(z0)))) A__ADD(s(fact(0)), x1) -> c3(A__ADD(a__fact(0), mark(x1)), MARK(fact(0))) A__ADD(s(fact(true)), x1) -> c3(A__ADD(a__fact(true), mark(x1)), MARK(fact(true))) A__ADD(s(fact(false)), x1) -> c3(A__ADD(a__fact(false), mark(x1)), MARK(fact(false))) A__ADD(s(fact(x0)), x1) -> c3(MARK(fact(x0))) A__ADD(s(if(fact(z0), x1, x2)), x3) -> c3(A__ADD(a__if(a__fact(mark(z0)), x1, x2), mark(x3)), MARK(if(fact(z0), x1, x2))) A__ADD(s(if(if(z0, z1, z2), x1, x2)), x3) -> c3(A__ADD(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(if(if(z0, z1, z2), x1, x2))) A__ADD(s(if(zero(z0), x1, x2)), x3) -> c3(A__ADD(a__if(a__zero(mark(z0)), x1, x2), mark(x3)), MARK(if(zero(z0), x1, x2))) A__ADD(s(if(prod(z0, z1), x1, x2)), x3) -> c3(A__ADD(a__if(a__prod(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(prod(z0, z1), x1, x2))) A__ADD(s(if(p(z0), x1, x2)), x3) -> c3(A__ADD(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(if(p(z0), x1, x2))) A__ADD(s(if(add(z0, z1), x1, x2)), x3) -> c3(A__ADD(a__if(a__add(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(add(z0, z1), x1, x2))) A__ADD(s(if(s(z0), x1, x2)), x3) -> c3(A__ADD(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(if(s(z0), x1, x2))) A__ADD(s(if(true, x1, x2)), x3) -> c3(A__ADD(a__if(true, x1, x2), mark(x3)), MARK(if(true, x1, x2))) A__ADD(s(if(false, x1, x2)), x3) -> c3(A__ADD(a__if(false, x1, x2), mark(x3)), MARK(if(false, x1, x2))) A__ADD(s(if(x0, z1, z2)), x3) -> c3(MARK(if(x0, z1, z2))) A__ADD(s(if(0, x1, x2)), x3) -> c3(A__ADD(a__if(0, x1, x2), mark(x3))) A__ADD(s(zero(fact(z0))), x1) -> c3(A__ADD(a__zero(a__fact(mark(z0))), mark(x1)), MARK(zero(fact(z0)))) A__ADD(s(zero(if(z0, z1, z2))), x1) -> c3(A__ADD(a__zero(a__if(mark(z0), z1, z2)), mark(x1)), MARK(zero(if(z0, z1, z2)))) A__ADD(s(zero(zero(z0))), x1) -> c3(A__ADD(a__zero(a__zero(mark(z0))), mark(x1)), MARK(zero(zero(z0)))) A__ADD(s(zero(prod(z0, z1))), x1) -> c3(A__ADD(a__zero(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(zero(prod(z0, z1)))) A__ADD(s(zero(p(z0))), x1) -> c3(A__ADD(a__zero(a__p(mark(z0))), mark(x1)), MARK(zero(p(z0)))) A__ADD(s(zero(add(z0, z1))), x1) -> c3(A__ADD(a__zero(a__add(mark(z0), mark(z1))), mark(x1)), MARK(zero(add(z0, z1)))) A__ADD(s(zero(s(z0))), x1) -> c3(A__ADD(a__zero(s(mark(z0))), mark(x1)), MARK(zero(s(z0)))) A__ADD(s(zero(0)), x1) -> c3(A__ADD(a__zero(0), mark(x1)), MARK(zero(0))) A__ADD(s(zero(true)), x1) -> c3(A__ADD(a__zero(true), mark(x1)), MARK(zero(true))) A__ADD(s(zero(false)), x1) -> c3(A__ADD(a__zero(false), mark(x1)), MARK(zero(false))) A__ADD(s(zero(x0)), x1) -> c3(MARK(zero(x0))) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1)))) A__ADD(s(x0), prod(x1, x2)) -> c3(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), prod(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, p(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, s(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, 0)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), prod(x1, true)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(x0)) A__ADD(s(x0), prod(x1, false)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(x0)) A__ADD(s(x0), prod(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(p(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(0, x2)) -> c3(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(true, x2)) -> c3(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(false, x2)) -> c3(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), prod(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2)))) A__ADD(s(x0), p(x1)) -> c3(A__ADD(mark(x0), p(mark(x1))), MARK(x0)) A__ADD(s(x0), p(fact(z0))) -> c3(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), p(zero(z0))) -> c3(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(p(z0))) -> c3(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(add(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(s(z0))) -> c3(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(0)) -> c3(A__ADD(mark(x0), a__p(0)), MARK(x0)) A__ADD(s(x0), p(true)) -> c3(A__ADD(mark(x0), a__p(true)), MARK(x0)) A__ADD(s(x0), p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1)))) A__ADD(s(x0), add(x1, x2)) -> c3(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), add(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), add(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, p(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, s(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, 0)) -> c3(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), add(x1, true)) -> c3(A__ADD(mark(x0), a__add(mark(x1), true)), MARK(x0)) A__ADD(s(x0), add(x1, false)) -> c3(A__ADD(mark(x0), a__add(mark(x1), false)), MARK(x0)) A__ADD(s(x0), add(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), add(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(p(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(s(z0), x2)) -> c3(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(0, x2)) -> c3(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) A__ADD(s(x0), add(true, x2)) -> c3(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(x0)) A__ADD(s(x0), add(false, x2)) -> c3(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), add(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), add(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), add(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__add(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), add(x1, x2)) -> c3(A__ADD(0, a__add(mark(x1), mark(x2)))) A__ADD(s(x0), s(fact(z0))) -> c3(A__ADD(mark(x0), s(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), s(zero(z0))) -> c3(A__ADD(mark(x0), s(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(prod(z0, z1))) -> c3(A__ADD(mark(x0), s(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(p(z0))) -> c3(A__ADD(mark(x0), s(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(add(z0, z1))) -> c3(A__ADD(mark(x0), s(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(s(z0))) -> c3(A__ADD(mark(x0), s(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(0)) -> c3(A__ADD(mark(x0), s(0)), MARK(x0)) A__ADD(s(x0), s(true)) -> c3(A__ADD(mark(x0), s(true)), MARK(x0)) A__ADD(s(x0), s(false)) -> c3(A__ADD(mark(x0), s(false)), MARK(x0)) A__ADD(s(fact(z0)), s(x1)) -> c3(A__ADD(a__fact(mark(z0)), s(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), s(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), s(x1)) -> c3(A__ADD(a__zero(mark(z0)), s(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), s(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), s(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), s(x1)) -> c3(A__ADD(a__p(mark(z0)), s(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), s(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), s(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), s(x1)) -> c3(A__ADD(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__ADD(s(0), s(x1)) -> c3(A__ADD(0, s(mark(x1)))) A__ADD(s(fact(z0)), 0) -> c3(A__ADD(a__fact(mark(z0)), 0), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), 0) -> c3(A__ADD(a__if(mark(z0), z1, z2), 0), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), 0) -> c3(A__ADD(a__zero(mark(z0)), 0), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), 0) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), 0), MARK(prod(z0, z1))) A__ADD(s(p(z0)), 0) -> c3(A__ADD(a__p(mark(z0)), 0), MARK(p(z0))) A__ADD(s(add(z0, z1)), 0) -> c3(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) A__ADD(s(s(z0)), 0) -> c3(A__ADD(s(mark(z0)), 0), MARK(s(z0))) A__ADD(s(0), 0) -> c3(A__ADD(0, 0)) A__ADD(s(fact(z0)), true) -> c3(A__ADD(a__fact(mark(z0)), true), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), true) -> c3(A__ADD(a__if(mark(z0), z1, z2), true), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), true) -> c3(A__ADD(a__zero(mark(z0)), true), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), true) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), true), MARK(prod(z0, z1))) A__ADD(s(p(z0)), true) -> c3(A__ADD(a__p(mark(z0)), true), MARK(p(z0))) A__ADD(s(add(z0, z1)), true) -> c3(A__ADD(a__add(mark(z0), mark(z1)), true), MARK(add(z0, z1))) A__ADD(s(s(z0)), true) -> c3(A__ADD(s(mark(z0)), true), MARK(s(z0))) A__ADD(s(0), true) -> c3(A__ADD(0, true)) A__ADD(s(fact(z0)), false) -> c3(A__ADD(a__fact(mark(z0)), false), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), false) -> c3(A__ADD(a__if(mark(z0), z1, z2), false), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), false) -> c3(A__ADD(a__zero(mark(z0)), false), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), false) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), false), MARK(prod(z0, z1))) A__ADD(s(p(z0)), false) -> c3(A__ADD(a__p(mark(z0)), false), MARK(p(z0))) A__ADD(s(add(z0, z1)), false) -> c3(A__ADD(a__add(mark(z0), mark(z1)), false), MARK(add(z0, z1))) A__ADD(s(s(z0)), false) -> c3(A__ADD(s(mark(z0)), false), MARK(s(z0))) A__ADD(s(0), false) -> c3(A__ADD(0, false)) A__ADD(s(fact(x0)), x1) -> c3(A__ADD(a__if(a__zero(mark(mark(x0))), s(0), prod(mark(x0), fact(p(mark(x0))))), mark(x1)), MARK(fact(x0))) A__ADD(s(fact(fact(z0))), x1) -> c3(A__ADD(a__fact(a__fact(mark(z0))), mark(x1)), MARK(fact(fact(z0)))) A__ADD(s(fact(if(z0, z1, z2))), x1) -> c3(A__ADD(a__fact(a__if(mark(z0), z1, z2)), mark(x1)), MARK(fact(if(z0, z1, z2)))) A__ADD(s(fact(zero(z0))), x1) -> c3(A__ADD(a__fact(a__zero(mark(z0))), mark(x1)), MARK(fact(zero(z0)))) A__ADD(s(fact(prod(z0, z1))), x1) -> c3(A__ADD(a__fact(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(fact(prod(z0, z1)))) A__ADD(s(fact(p(z0))), x1) -> c3(A__ADD(a__fact(a__p(mark(z0))), mark(x1)), MARK(fact(p(z0)))) A__ADD(s(fact(add(z0, z1))), x1) -> c3(A__ADD(a__fact(a__add(mark(z0), mark(z1))), mark(x1)), MARK(fact(add(z0, z1)))) A__ADD(s(fact(s(z0))), x1) -> c3(A__ADD(a__fact(s(mark(z0))), mark(x1)), MARK(fact(s(z0)))) A__ADD(s(fact(0)), x1) -> c3(A__ADD(a__fact(0), mark(x1)), MARK(fact(0))) A__ADD(s(fact(true)), x1) -> c3(A__ADD(a__fact(true), mark(x1)), MARK(fact(true))) A__ADD(s(fact(false)), x1) -> c3(A__ADD(a__fact(false), mark(x1)), MARK(fact(false))) A__ADD(s(fact(x0)), x1) -> c3(MARK(fact(x0))) A__ADD(s(if(fact(z0), x1, x2)), x3) -> c3(A__ADD(a__if(a__fact(mark(z0)), x1, x2), mark(x3)), MARK(if(fact(z0), x1, x2))) A__ADD(s(if(if(z0, z1, z2), x1, x2)), x3) -> c3(A__ADD(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(if(if(z0, z1, z2), x1, x2))) A__ADD(s(if(zero(z0), x1, x2)), x3) -> c3(A__ADD(a__if(a__zero(mark(z0)), x1, x2), mark(x3)), MARK(if(zero(z0), x1, x2))) A__ADD(s(if(prod(z0, z1), x1, x2)), x3) -> c3(A__ADD(a__if(a__prod(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(prod(z0, z1), x1, x2))) A__ADD(s(if(p(z0), x1, x2)), x3) -> c3(A__ADD(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(if(p(z0), x1, x2))) A__ADD(s(if(add(z0, z1), x1, x2)), x3) -> c3(A__ADD(a__if(a__add(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(add(z0, z1), x1, x2))) A__ADD(s(if(s(z0), x1, x2)), x3) -> c3(A__ADD(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(if(s(z0), x1, x2))) A__ADD(s(if(true, x1, x2)), x3) -> c3(A__ADD(a__if(true, x1, x2), mark(x3)), MARK(if(true, x1, x2))) A__ADD(s(if(false, x1, x2)), x3) -> c3(A__ADD(a__if(false, x1, x2), mark(x3)), MARK(if(false, x1, x2))) A__ADD(s(if(x0, z1, z2)), x3) -> c3(MARK(if(x0, z1, z2))) A__ADD(s(if(0, x1, x2)), x3) -> c3(A__ADD(a__if(0, x1, x2), mark(x3))) A__ADD(s(zero(fact(z0))), x1) -> c3(A__ADD(a__zero(a__fact(mark(z0))), mark(x1)), MARK(zero(fact(z0)))) A__ADD(s(zero(if(z0, z1, z2))), x1) -> c3(A__ADD(a__zero(a__if(mark(z0), z1, z2)), mark(x1)), MARK(zero(if(z0, z1, z2)))) A__ADD(s(zero(zero(z0))), x1) -> c3(A__ADD(a__zero(a__zero(mark(z0))), mark(x1)), MARK(zero(zero(z0)))) A__ADD(s(zero(prod(z0, z1))), x1) -> c3(A__ADD(a__zero(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(zero(prod(z0, z1)))) A__ADD(s(zero(p(z0))), x1) -> c3(A__ADD(a__zero(a__p(mark(z0))), mark(x1)), MARK(zero(p(z0)))) A__ADD(s(zero(add(z0, z1))), x1) -> c3(A__ADD(a__zero(a__add(mark(z0), mark(z1))), mark(x1)), MARK(zero(add(z0, z1)))) A__ADD(s(zero(s(z0))), x1) -> c3(A__ADD(a__zero(s(mark(z0))), mark(x1)), MARK(zero(s(z0)))) A__ADD(s(zero(0)), x1) -> c3(A__ADD(a__zero(0), mark(x1)), MARK(zero(0))) A__ADD(s(zero(true)), x1) -> c3(A__ADD(a__zero(true), mark(x1)), MARK(zero(true))) A__ADD(s(zero(false)), x1) -> c3(A__ADD(a__zero(false), mark(x1)), MARK(zero(false))) A__ADD(s(zero(x0)), x1) -> c3(MARK(zero(x0))) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__PROD_2, A__FACT_1 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c27_1, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1, c24_2, c25_2, c25_1, c26_2, c26_1, c_2, c_1 ---------------------------------------- (197) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__ADD(s(prod(z0, z1)), x1) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) by A__ADD(s(prod(x0, x1)), fact(z0)) -> c3(A__ADD(a__prod(mark(x0), mark(x1)), a__fact(mark(z0))), MARK(prod(x0, x1))) A__ADD(s(prod(x0, x1)), if(z0, z1, z2)) -> c3(A__ADD(a__prod(mark(x0), mark(x1)), a__if(mark(z0), z1, z2)), MARK(prod(x0, x1))) A__ADD(s(prod(x0, x1)), zero(z0)) -> c3(A__ADD(a__prod(mark(x0), mark(x1)), a__zero(mark(z0))), MARK(prod(x0, x1))) A__ADD(s(prod(x0, x1)), prod(z0, z1)) -> c3(A__ADD(a__prod(mark(x0), mark(x1)), a__prod(mark(z0), mark(z1))), MARK(prod(x0, x1))) A__ADD(s(prod(x0, x1)), p(z0)) -> c3(A__ADD(a__prod(mark(x0), mark(x1)), a__p(mark(z0))), MARK(prod(x0, x1))) A__ADD(s(prod(x0, x1)), add(z0, z1)) -> c3(A__ADD(a__prod(mark(x0), mark(x1)), a__add(mark(z0), mark(z1))), MARK(prod(x0, x1))) A__ADD(s(prod(x0, x1)), s(z0)) -> c3(A__ADD(a__prod(mark(x0), mark(x1)), s(mark(z0))), MARK(prod(x0, x1))) A__ADD(s(prod(x0, x1)), 0) -> c3(A__ADD(a__prod(mark(x0), mark(x1)), 0), MARK(prod(x0, x1))) A__ADD(s(prod(x0, x1)), true) -> c3(A__ADD(a__prod(mark(x0), mark(x1)), true), MARK(prod(x0, x1))) A__ADD(s(prod(x0, x1)), false) -> c3(A__ADD(a__prod(mark(x0), mark(x1)), false), MARK(prod(x0, x1))) A__ADD(s(prod(x0, x1)), x2) -> c3(A__ADD(prod(mark(x0), mark(x1)), mark(x2)), MARK(prod(x0, x1))) A__ADD(s(prod(x0, fact(z0))), x2) -> c3(A__ADD(a__prod(mark(x0), a__fact(mark(z0))), mark(x2)), MARK(prod(x0, fact(z0)))) A__ADD(s(prod(x0, if(z0, z1, z2))), x2) -> c3(A__ADD(a__prod(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(prod(x0, if(z0, z1, z2)))) A__ADD(s(prod(x0, zero(z0))), x2) -> c3(A__ADD(a__prod(mark(x0), a__zero(mark(z0))), mark(x2)), MARK(prod(x0, zero(z0)))) A__ADD(s(prod(x0, prod(z0, z1))), x2) -> c3(A__ADD(a__prod(mark(x0), a__prod(mark(z0), mark(z1))), mark(x2)), MARK(prod(x0, prod(z0, z1)))) A__ADD(s(prod(x0, p(z0))), x2) -> c3(A__ADD(a__prod(mark(x0), a__p(mark(z0))), mark(x2)), MARK(prod(x0, p(z0)))) A__ADD(s(prod(x0, add(z0, z1))), x2) -> c3(A__ADD(a__prod(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(prod(x0, add(z0, z1)))) A__ADD(s(prod(x0, s(z0))), x2) -> c3(A__ADD(a__prod(mark(x0), s(mark(z0))), mark(x2)), MARK(prod(x0, s(z0)))) A__ADD(s(prod(x0, 0)), x2) -> c3(A__ADD(a__prod(mark(x0), 0), mark(x2)), MARK(prod(x0, 0))) A__ADD(s(prod(x0, true)), x2) -> c3(A__ADD(a__prod(mark(x0), true), mark(x2)), MARK(prod(x0, true))) A__ADD(s(prod(x0, false)), x2) -> c3(A__ADD(a__prod(mark(x0), false), mark(x2)), MARK(prod(x0, false))) A__ADD(s(prod(fact(z0), x1)), x2) -> c3(A__ADD(a__prod(a__fact(mark(z0)), mark(x1)), mark(x2)), MARK(prod(fact(z0), x1))) A__ADD(s(prod(if(z0, z1, z2), x1)), x2) -> c3(A__ADD(a__prod(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(prod(if(z0, z1, z2), x1))) A__ADD(s(prod(zero(z0), x1)), x2) -> c3(A__ADD(a__prod(a__zero(mark(z0)), mark(x1)), mark(x2)), MARK(prod(zero(z0), x1))) A__ADD(s(prod(prod(z0, z1), x1)), x2) -> c3(A__ADD(a__prod(a__prod(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(prod(prod(z0, z1), x1))) A__ADD(s(prod(p(z0), x1)), x2) -> c3(A__ADD(a__prod(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(prod(p(z0), x1))) A__ADD(s(prod(add(z0, z1), x1)), x2) -> c3(A__ADD(a__prod(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(prod(add(z0, z1), x1))) A__ADD(s(prod(s(z0), x1)), x2) -> c3(A__ADD(a__prod(s(mark(z0)), mark(x1)), mark(x2)), MARK(prod(s(z0), x1))) A__ADD(s(prod(0, x1)), x2) -> c3(A__ADD(a__prod(0, mark(x1)), mark(x2)), MARK(prod(0, x1))) A__ADD(s(prod(true, x1)), x2) -> c3(A__ADD(a__prod(true, mark(x1)), mark(x2)), MARK(prod(true, x1))) A__ADD(s(prod(false, x1)), x2) -> c3(A__ADD(a__prod(false, mark(x1)), mark(x2)), MARK(prod(false, x1))) ---------------------------------------- (198) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1)))) A__ADD(s(x0), prod(x1, x2)) -> c3(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), prod(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, p(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, s(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, 0)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), prod(x1, true)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(x0)) A__ADD(s(x0), prod(x1, false)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(x0)) A__ADD(s(x0), prod(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(p(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(0, x2)) -> c3(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(true, x2)) -> c3(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(false, x2)) -> c3(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), prod(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2)))) A__ADD(s(x0), p(x1)) -> c3(A__ADD(mark(x0), p(mark(x1))), MARK(x0)) A__ADD(s(x0), p(fact(z0))) -> c3(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), p(zero(z0))) -> c3(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(p(z0))) -> c3(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(add(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(s(z0))) -> c3(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(0)) -> c3(A__ADD(mark(x0), a__p(0)), MARK(x0)) A__ADD(s(x0), p(true)) -> c3(A__ADD(mark(x0), a__p(true)), MARK(x0)) A__ADD(s(x0), p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1)))) A__ADD(s(x0), add(x1, x2)) -> c3(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), add(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), add(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, p(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, s(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, 0)) -> c3(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), add(x1, true)) -> c3(A__ADD(mark(x0), a__add(mark(x1), true)), MARK(x0)) A__ADD(s(x0), add(x1, false)) -> c3(A__ADD(mark(x0), a__add(mark(x1), false)), MARK(x0)) A__ADD(s(x0), add(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), add(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(p(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(s(z0), x2)) -> c3(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(0, x2)) -> c3(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) A__ADD(s(x0), add(true, x2)) -> c3(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(x0)) A__ADD(s(x0), add(false, x2)) -> c3(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), add(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), add(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), add(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__add(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), add(x1, x2)) -> c3(A__ADD(0, a__add(mark(x1), mark(x2)))) A__ADD(s(x0), s(fact(z0))) -> c3(A__ADD(mark(x0), s(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), s(zero(z0))) -> c3(A__ADD(mark(x0), s(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(prod(z0, z1))) -> c3(A__ADD(mark(x0), s(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(p(z0))) -> c3(A__ADD(mark(x0), s(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(add(z0, z1))) -> c3(A__ADD(mark(x0), s(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(s(z0))) -> c3(A__ADD(mark(x0), s(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(0)) -> c3(A__ADD(mark(x0), s(0)), MARK(x0)) A__ADD(s(x0), s(true)) -> c3(A__ADD(mark(x0), s(true)), MARK(x0)) A__ADD(s(x0), s(false)) -> c3(A__ADD(mark(x0), s(false)), MARK(x0)) A__ADD(s(fact(z0)), s(x1)) -> c3(A__ADD(a__fact(mark(z0)), s(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), s(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), s(x1)) -> c3(A__ADD(a__zero(mark(z0)), s(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), s(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), s(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), s(x1)) -> c3(A__ADD(a__p(mark(z0)), s(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), s(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), s(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), s(x1)) -> c3(A__ADD(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__ADD(s(0), s(x1)) -> c3(A__ADD(0, s(mark(x1)))) A__ADD(s(fact(z0)), 0) -> c3(A__ADD(a__fact(mark(z0)), 0), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), 0) -> c3(A__ADD(a__if(mark(z0), z1, z2), 0), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), 0) -> c3(A__ADD(a__zero(mark(z0)), 0), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), 0) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), 0), MARK(prod(z0, z1))) A__ADD(s(p(z0)), 0) -> c3(A__ADD(a__p(mark(z0)), 0), MARK(p(z0))) A__ADD(s(add(z0, z1)), 0) -> c3(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) A__ADD(s(s(z0)), 0) -> c3(A__ADD(s(mark(z0)), 0), MARK(s(z0))) A__ADD(s(0), 0) -> c3(A__ADD(0, 0)) A__ADD(s(fact(z0)), true) -> c3(A__ADD(a__fact(mark(z0)), true), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), true) -> c3(A__ADD(a__if(mark(z0), z1, z2), true), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), true) -> c3(A__ADD(a__zero(mark(z0)), true), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), true) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), true), MARK(prod(z0, z1))) A__ADD(s(p(z0)), true) -> c3(A__ADD(a__p(mark(z0)), true), MARK(p(z0))) A__ADD(s(add(z0, z1)), true) -> c3(A__ADD(a__add(mark(z0), mark(z1)), true), MARK(add(z0, z1))) A__ADD(s(s(z0)), true) -> c3(A__ADD(s(mark(z0)), true), MARK(s(z0))) A__ADD(s(0), true) -> c3(A__ADD(0, true)) A__ADD(s(fact(z0)), false) -> c3(A__ADD(a__fact(mark(z0)), false), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), false) -> c3(A__ADD(a__if(mark(z0), z1, z2), false), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), false) -> c3(A__ADD(a__zero(mark(z0)), false), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), false) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), false), MARK(prod(z0, z1))) A__ADD(s(p(z0)), false) -> c3(A__ADD(a__p(mark(z0)), false), MARK(p(z0))) A__ADD(s(add(z0, z1)), false) -> c3(A__ADD(a__add(mark(z0), mark(z1)), false), MARK(add(z0, z1))) A__ADD(s(s(z0)), false) -> c3(A__ADD(s(mark(z0)), false), MARK(s(z0))) A__ADD(s(0), false) -> c3(A__ADD(0, false)) A__ADD(s(fact(x0)), x1) -> c3(A__ADD(a__if(a__zero(mark(mark(x0))), s(0), prod(mark(x0), fact(p(mark(x0))))), mark(x1)), MARK(fact(x0))) A__ADD(s(fact(fact(z0))), x1) -> c3(A__ADD(a__fact(a__fact(mark(z0))), mark(x1)), MARK(fact(fact(z0)))) A__ADD(s(fact(if(z0, z1, z2))), x1) -> c3(A__ADD(a__fact(a__if(mark(z0), z1, z2)), mark(x1)), MARK(fact(if(z0, z1, z2)))) A__ADD(s(fact(zero(z0))), x1) -> c3(A__ADD(a__fact(a__zero(mark(z0))), mark(x1)), MARK(fact(zero(z0)))) A__ADD(s(fact(prod(z0, z1))), x1) -> c3(A__ADD(a__fact(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(fact(prod(z0, z1)))) A__ADD(s(fact(p(z0))), x1) -> c3(A__ADD(a__fact(a__p(mark(z0))), mark(x1)), MARK(fact(p(z0)))) A__ADD(s(fact(add(z0, z1))), x1) -> c3(A__ADD(a__fact(a__add(mark(z0), mark(z1))), mark(x1)), MARK(fact(add(z0, z1)))) A__ADD(s(fact(s(z0))), x1) -> c3(A__ADD(a__fact(s(mark(z0))), mark(x1)), MARK(fact(s(z0)))) A__ADD(s(fact(0)), x1) -> c3(A__ADD(a__fact(0), mark(x1)), MARK(fact(0))) A__ADD(s(fact(true)), x1) -> c3(A__ADD(a__fact(true), mark(x1)), MARK(fact(true))) A__ADD(s(fact(false)), x1) -> c3(A__ADD(a__fact(false), mark(x1)), MARK(fact(false))) A__ADD(s(fact(x0)), x1) -> c3(MARK(fact(x0))) A__ADD(s(if(fact(z0), x1, x2)), x3) -> c3(A__ADD(a__if(a__fact(mark(z0)), x1, x2), mark(x3)), MARK(if(fact(z0), x1, x2))) A__ADD(s(if(if(z0, z1, z2), x1, x2)), x3) -> c3(A__ADD(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(if(if(z0, z1, z2), x1, x2))) A__ADD(s(if(zero(z0), x1, x2)), x3) -> c3(A__ADD(a__if(a__zero(mark(z0)), x1, x2), mark(x3)), MARK(if(zero(z0), x1, x2))) A__ADD(s(if(prod(z0, z1), x1, x2)), x3) -> c3(A__ADD(a__if(a__prod(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(prod(z0, z1), x1, x2))) A__ADD(s(if(p(z0), x1, x2)), x3) -> c3(A__ADD(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(if(p(z0), x1, x2))) A__ADD(s(if(add(z0, z1), x1, x2)), x3) -> c3(A__ADD(a__if(a__add(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(add(z0, z1), x1, x2))) A__ADD(s(if(s(z0), x1, x2)), x3) -> c3(A__ADD(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(if(s(z0), x1, x2))) A__ADD(s(if(true, x1, x2)), x3) -> c3(A__ADD(a__if(true, x1, x2), mark(x3)), MARK(if(true, x1, x2))) A__ADD(s(if(false, x1, x2)), x3) -> c3(A__ADD(a__if(false, x1, x2), mark(x3)), MARK(if(false, x1, x2))) A__ADD(s(if(x0, z1, z2)), x3) -> c3(MARK(if(x0, z1, z2))) A__ADD(s(if(0, x1, x2)), x3) -> c3(A__ADD(a__if(0, x1, x2), mark(x3))) A__ADD(s(zero(fact(z0))), x1) -> c3(A__ADD(a__zero(a__fact(mark(z0))), mark(x1)), MARK(zero(fact(z0)))) A__ADD(s(zero(if(z0, z1, z2))), x1) -> c3(A__ADD(a__zero(a__if(mark(z0), z1, z2)), mark(x1)), MARK(zero(if(z0, z1, z2)))) A__ADD(s(zero(zero(z0))), x1) -> c3(A__ADD(a__zero(a__zero(mark(z0))), mark(x1)), MARK(zero(zero(z0)))) A__ADD(s(zero(prod(z0, z1))), x1) -> c3(A__ADD(a__zero(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(zero(prod(z0, z1)))) A__ADD(s(zero(p(z0))), x1) -> c3(A__ADD(a__zero(a__p(mark(z0))), mark(x1)), MARK(zero(p(z0)))) A__ADD(s(zero(add(z0, z1))), x1) -> c3(A__ADD(a__zero(a__add(mark(z0), mark(z1))), mark(x1)), MARK(zero(add(z0, z1)))) A__ADD(s(zero(s(z0))), x1) -> c3(A__ADD(a__zero(s(mark(z0))), mark(x1)), MARK(zero(s(z0)))) A__ADD(s(zero(0)), x1) -> c3(A__ADD(a__zero(0), mark(x1)), MARK(zero(0))) A__ADD(s(zero(true)), x1) -> c3(A__ADD(a__zero(true), mark(x1)), MARK(zero(true))) A__ADD(s(zero(false)), x1) -> c3(A__ADD(a__zero(false), mark(x1)), MARK(zero(false))) A__ADD(s(zero(x0)), x1) -> c3(MARK(zero(x0))) A__ADD(s(prod(x0, x1)), x2) -> c3(A__ADD(prod(mark(x0), mark(x1)), mark(x2)), MARK(prod(x0, x1))) A__ADD(s(prod(x0, fact(z0))), x2) -> c3(A__ADD(a__prod(mark(x0), a__fact(mark(z0))), mark(x2)), MARK(prod(x0, fact(z0)))) A__ADD(s(prod(x0, if(z0, z1, z2))), x2) -> c3(A__ADD(a__prod(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(prod(x0, if(z0, z1, z2)))) A__ADD(s(prod(x0, zero(z0))), x2) -> c3(A__ADD(a__prod(mark(x0), a__zero(mark(z0))), mark(x2)), MARK(prod(x0, zero(z0)))) A__ADD(s(prod(x0, prod(z0, z1))), x2) -> c3(A__ADD(a__prod(mark(x0), a__prod(mark(z0), mark(z1))), mark(x2)), MARK(prod(x0, prod(z0, z1)))) A__ADD(s(prod(x0, p(z0))), x2) -> c3(A__ADD(a__prod(mark(x0), a__p(mark(z0))), mark(x2)), MARK(prod(x0, p(z0)))) A__ADD(s(prod(x0, add(z0, z1))), x2) -> c3(A__ADD(a__prod(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(prod(x0, add(z0, z1)))) A__ADD(s(prod(x0, s(z0))), x2) -> c3(A__ADD(a__prod(mark(x0), s(mark(z0))), mark(x2)), MARK(prod(x0, s(z0)))) A__ADD(s(prod(x0, 0)), x2) -> c3(A__ADD(a__prod(mark(x0), 0), mark(x2)), MARK(prod(x0, 0))) A__ADD(s(prod(x0, true)), x2) -> c3(A__ADD(a__prod(mark(x0), true), mark(x2)), MARK(prod(x0, true))) A__ADD(s(prod(x0, false)), x2) -> c3(A__ADD(a__prod(mark(x0), false), mark(x2)), MARK(prod(x0, false))) A__ADD(s(prod(fact(z0), x1)), x2) -> c3(A__ADD(a__prod(a__fact(mark(z0)), mark(x1)), mark(x2)), MARK(prod(fact(z0), x1))) A__ADD(s(prod(if(z0, z1, z2), x1)), x2) -> c3(A__ADD(a__prod(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(prod(if(z0, z1, z2), x1))) A__ADD(s(prod(zero(z0), x1)), x2) -> c3(A__ADD(a__prod(a__zero(mark(z0)), mark(x1)), mark(x2)), MARK(prod(zero(z0), x1))) A__ADD(s(prod(prod(z0, z1), x1)), x2) -> c3(A__ADD(a__prod(a__prod(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(prod(prod(z0, z1), x1))) A__ADD(s(prod(p(z0), x1)), x2) -> c3(A__ADD(a__prod(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(prod(p(z0), x1))) A__ADD(s(prod(add(z0, z1), x1)), x2) -> c3(A__ADD(a__prod(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(prod(add(z0, z1), x1))) A__ADD(s(prod(s(z0), x1)), x2) -> c3(A__ADD(a__prod(s(mark(z0)), mark(x1)), mark(x2)), MARK(prod(s(z0), x1))) A__ADD(s(prod(0, x1)), x2) -> c3(A__ADD(a__prod(0, mark(x1)), mark(x2)), MARK(prod(0, x1))) A__ADD(s(prod(true, x1)), x2) -> c3(A__ADD(a__prod(true, mark(x1)), mark(x2)), MARK(prod(true, x1))) A__ADD(s(prod(false, x1)), x2) -> c3(A__ADD(a__prod(false, mark(x1)), mark(x2)), MARK(prod(false, x1))) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, 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c3(A__ADD(mark(x0), a__p(0)), MARK(x0)) A__ADD(s(x0), p(true)) -> c3(A__ADD(mark(x0), a__p(true)), MARK(x0)) A__ADD(s(x0), p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1)))) A__ADD(s(x0), add(x1, x2)) -> c3(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), add(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), add(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, p(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, s(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, 0)) -> c3(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), add(x1, true)) -> c3(A__ADD(mark(x0), a__add(mark(x1), true)), MARK(x0)) A__ADD(s(x0), add(x1, false)) -> c3(A__ADD(mark(x0), a__add(mark(x1), false)), MARK(x0)) A__ADD(s(x0), add(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), add(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(p(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(s(z0), x2)) -> c3(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(0, x2)) -> c3(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) A__ADD(s(x0), add(true, x2)) -> c3(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(x0)) A__ADD(s(x0), add(false, x2)) -> c3(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), add(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), add(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), add(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__add(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), add(x1, x2)) -> c3(A__ADD(0, a__add(mark(x1), mark(x2)))) A__ADD(s(x0), s(fact(z0))) -> c3(A__ADD(mark(x0), s(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), s(zero(z0))) -> c3(A__ADD(mark(x0), s(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(prod(z0, z1))) -> c3(A__ADD(mark(x0), s(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(p(z0))) -> c3(A__ADD(mark(x0), s(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(add(z0, z1))) -> c3(A__ADD(mark(x0), s(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(s(z0))) -> c3(A__ADD(mark(x0), s(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(0)) -> c3(A__ADD(mark(x0), s(0)), MARK(x0)) A__ADD(s(x0), s(true)) -> c3(A__ADD(mark(x0), s(true)), MARK(x0)) A__ADD(s(x0), s(false)) -> c3(A__ADD(mark(x0), s(false)), MARK(x0)) A__ADD(s(fact(z0)), s(x1)) -> c3(A__ADD(a__fact(mark(z0)), s(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), s(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), s(x1)) -> c3(A__ADD(a__zero(mark(z0)), s(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), s(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), s(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), s(x1)) -> c3(A__ADD(a__p(mark(z0)), s(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), s(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), s(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), s(x1)) -> c3(A__ADD(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__ADD(s(0), s(x1)) -> c3(A__ADD(0, s(mark(x1)))) A__ADD(s(fact(z0)), 0) -> c3(A__ADD(a__fact(mark(z0)), 0), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), 0) -> c3(A__ADD(a__if(mark(z0), z1, z2), 0), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), 0) -> c3(A__ADD(a__zero(mark(z0)), 0), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), 0) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), 0), MARK(prod(z0, z1))) A__ADD(s(p(z0)), 0) -> c3(A__ADD(a__p(mark(z0)), 0), MARK(p(z0))) A__ADD(s(add(z0, z1)), 0) -> c3(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) A__ADD(s(s(z0)), 0) -> c3(A__ADD(s(mark(z0)), 0), MARK(s(z0))) A__ADD(s(0), 0) -> c3(A__ADD(0, 0)) A__ADD(s(fact(z0)), true) -> c3(A__ADD(a__fact(mark(z0)), true), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), true) -> c3(A__ADD(a__if(mark(z0), z1, z2), true), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), true) -> c3(A__ADD(a__zero(mark(z0)), true), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), true) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), true), MARK(prod(z0, z1))) A__ADD(s(p(z0)), true) -> c3(A__ADD(a__p(mark(z0)), true), MARK(p(z0))) A__ADD(s(add(z0, z1)), true) -> c3(A__ADD(a__add(mark(z0), mark(z1)), true), MARK(add(z0, z1))) A__ADD(s(s(z0)), true) -> c3(A__ADD(s(mark(z0)), true), MARK(s(z0))) A__ADD(s(0), true) -> c3(A__ADD(0, true)) A__ADD(s(fact(z0)), false) -> c3(A__ADD(a__fact(mark(z0)), false), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), false) -> c3(A__ADD(a__if(mark(z0), z1, z2), false), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), false) -> c3(A__ADD(a__zero(mark(z0)), false), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), false) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), false), MARK(prod(z0, z1))) A__ADD(s(p(z0)), false) -> c3(A__ADD(a__p(mark(z0)), false), MARK(p(z0))) A__ADD(s(add(z0, z1)), false) -> c3(A__ADD(a__add(mark(z0), mark(z1)), false), MARK(add(z0, z1))) A__ADD(s(s(z0)), false) -> c3(A__ADD(s(mark(z0)), false), MARK(s(z0))) A__ADD(s(0), false) -> c3(A__ADD(0, false)) A__ADD(s(fact(x0)), x1) -> c3(A__ADD(a__if(a__zero(mark(mark(x0))), s(0), prod(mark(x0), fact(p(mark(x0))))), mark(x1)), MARK(fact(x0))) A__ADD(s(fact(fact(z0))), x1) -> c3(A__ADD(a__fact(a__fact(mark(z0))), mark(x1)), MARK(fact(fact(z0)))) A__ADD(s(fact(if(z0, z1, z2))), x1) -> c3(A__ADD(a__fact(a__if(mark(z0), z1, z2)), mark(x1)), MARK(fact(if(z0, z1, z2)))) A__ADD(s(fact(zero(z0))), x1) -> c3(A__ADD(a__fact(a__zero(mark(z0))), mark(x1)), MARK(fact(zero(z0)))) A__ADD(s(fact(prod(z0, z1))), x1) -> c3(A__ADD(a__fact(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(fact(prod(z0, z1)))) A__ADD(s(fact(p(z0))), x1) -> c3(A__ADD(a__fact(a__p(mark(z0))), mark(x1)), MARK(fact(p(z0)))) A__ADD(s(fact(add(z0, z1))), x1) -> c3(A__ADD(a__fact(a__add(mark(z0), mark(z1))), mark(x1)), MARK(fact(add(z0, z1)))) A__ADD(s(fact(s(z0))), x1) -> c3(A__ADD(a__fact(s(mark(z0))), mark(x1)), MARK(fact(s(z0)))) A__ADD(s(fact(0)), x1) -> c3(A__ADD(a__fact(0), mark(x1)), MARK(fact(0))) A__ADD(s(fact(true)), x1) -> c3(A__ADD(a__fact(true), mark(x1)), MARK(fact(true))) A__ADD(s(fact(false)), x1) -> c3(A__ADD(a__fact(false), mark(x1)), MARK(fact(false))) A__ADD(s(fact(x0)), x1) -> c3(MARK(fact(x0))) A__ADD(s(if(fact(z0), x1, x2)), x3) -> c3(A__ADD(a__if(a__fact(mark(z0)), x1, x2), mark(x3)), MARK(if(fact(z0), x1, x2))) A__ADD(s(if(if(z0, z1, z2), x1, x2)), x3) -> c3(A__ADD(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(if(if(z0, z1, z2), x1, x2))) A__ADD(s(if(zero(z0), x1, x2)), x3) -> c3(A__ADD(a__if(a__zero(mark(z0)), x1, x2), mark(x3)), MARK(if(zero(z0), x1, x2))) A__ADD(s(if(prod(z0, z1), x1, x2)), x3) -> c3(A__ADD(a__if(a__prod(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(prod(z0, z1), x1, x2))) A__ADD(s(if(p(z0), x1, x2)), x3) -> c3(A__ADD(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(if(p(z0), x1, x2))) A__ADD(s(if(add(z0, z1), x1, x2)), x3) -> c3(A__ADD(a__if(a__add(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(add(z0, z1), x1, x2))) A__ADD(s(if(s(z0), x1, x2)), x3) -> c3(A__ADD(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(if(s(z0), x1, x2))) A__ADD(s(if(true, x1, x2)), x3) -> c3(A__ADD(a__if(true, x1, x2), mark(x3)), MARK(if(true, x1, x2))) A__ADD(s(if(false, x1, x2)), x3) -> c3(A__ADD(a__if(false, x1, x2), mark(x3)), MARK(if(false, x1, x2))) A__ADD(s(if(x0, z1, z2)), x3) -> c3(MARK(if(x0, z1, z2))) A__ADD(s(if(0, x1, x2)), x3) -> c3(A__ADD(a__if(0, x1, x2), mark(x3))) A__ADD(s(zero(fact(z0))), x1) -> c3(A__ADD(a__zero(a__fact(mark(z0))), mark(x1)), MARK(zero(fact(z0)))) A__ADD(s(zero(if(z0, z1, z2))), x1) -> c3(A__ADD(a__zero(a__if(mark(z0), z1, z2)), mark(x1)), MARK(zero(if(z0, z1, z2)))) A__ADD(s(zero(zero(z0))), x1) -> c3(A__ADD(a__zero(a__zero(mark(z0))), mark(x1)), MARK(zero(zero(z0)))) A__ADD(s(zero(prod(z0, z1))), x1) -> c3(A__ADD(a__zero(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(zero(prod(z0, z1)))) A__ADD(s(zero(p(z0))), x1) -> c3(A__ADD(a__zero(a__p(mark(z0))), mark(x1)), MARK(zero(p(z0)))) A__ADD(s(zero(add(z0, z1))), x1) -> c3(A__ADD(a__zero(a__add(mark(z0), mark(z1))), mark(x1)), MARK(zero(add(z0, z1)))) A__ADD(s(zero(s(z0))), x1) -> c3(A__ADD(a__zero(s(mark(z0))), mark(x1)), MARK(zero(s(z0)))) A__ADD(s(zero(0)), x1) -> c3(A__ADD(a__zero(0), mark(x1)), MARK(zero(0))) A__ADD(s(zero(true)), x1) -> c3(A__ADD(a__zero(true), mark(x1)), MARK(zero(true))) A__ADD(s(zero(false)), x1) -> c3(A__ADD(a__zero(false), mark(x1)), MARK(zero(false))) A__ADD(s(zero(x0)), x1) -> c3(MARK(zero(x0))) A__ADD(s(prod(x0, x1)), x2) -> c3(A__ADD(prod(mark(x0), mark(x1)), mark(x2)), MARK(prod(x0, x1))) A__ADD(s(prod(x0, fact(z0))), x2) -> c3(A__ADD(a__prod(mark(x0), a__fact(mark(z0))), mark(x2)), MARK(prod(x0, fact(z0)))) A__ADD(s(prod(x0, if(z0, z1, z2))), x2) -> c3(A__ADD(a__prod(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(prod(x0, if(z0, z1, z2)))) A__ADD(s(prod(x0, zero(z0))), x2) -> c3(A__ADD(a__prod(mark(x0), a__zero(mark(z0))), mark(x2)), MARK(prod(x0, zero(z0)))) A__ADD(s(prod(x0, prod(z0, z1))), x2) -> c3(A__ADD(a__prod(mark(x0), a__prod(mark(z0), mark(z1))), mark(x2)), MARK(prod(x0, prod(z0, z1)))) A__ADD(s(prod(x0, p(z0))), x2) -> c3(A__ADD(a__prod(mark(x0), a__p(mark(z0))), mark(x2)), MARK(prod(x0, p(z0)))) A__ADD(s(prod(x0, add(z0, z1))), x2) -> c3(A__ADD(a__prod(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(prod(x0, add(z0, z1)))) A__ADD(s(prod(x0, s(z0))), x2) -> c3(A__ADD(a__prod(mark(x0), s(mark(z0))), mark(x2)), MARK(prod(x0, s(z0)))) A__ADD(s(prod(x0, 0)), x2) -> c3(A__ADD(a__prod(mark(x0), 0), mark(x2)), MARK(prod(x0, 0))) A__ADD(s(prod(x0, true)), x2) -> c3(A__ADD(a__prod(mark(x0), true), mark(x2)), MARK(prod(x0, true))) A__ADD(s(prod(x0, false)), x2) -> c3(A__ADD(a__prod(mark(x0), false), mark(x2)), MARK(prod(x0, false))) A__ADD(s(prod(fact(z0), x1)), x2) -> c3(A__ADD(a__prod(a__fact(mark(z0)), mark(x1)), mark(x2)), MARK(prod(fact(z0), x1))) A__ADD(s(prod(if(z0, z1, z2), x1)), x2) -> c3(A__ADD(a__prod(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(prod(if(z0, z1, z2), x1))) A__ADD(s(prod(zero(z0), x1)), x2) -> c3(A__ADD(a__prod(a__zero(mark(z0)), mark(x1)), mark(x2)), MARK(prod(zero(z0), x1))) A__ADD(s(prod(prod(z0, z1), x1)), x2) -> c3(A__ADD(a__prod(a__prod(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(prod(prod(z0, z1), x1))) A__ADD(s(prod(p(z0), x1)), x2) -> c3(A__ADD(a__prod(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(prod(p(z0), x1))) A__ADD(s(prod(add(z0, z1), x1)), x2) -> c3(A__ADD(a__prod(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(prod(add(z0, z1), x1))) A__ADD(s(prod(s(z0), x1)), x2) -> c3(A__ADD(a__prod(s(mark(z0)), mark(x1)), mark(x2)), MARK(prod(s(z0), x1))) A__ADD(s(prod(0, x1)), x2) -> c3(A__ADD(a__prod(0, mark(x1)), mark(x2)), MARK(prod(0, x1))) A__ADD(s(prod(true, x1)), x2) -> c3(A__ADD(a__prod(true, mark(x1)), mark(x2)), MARK(prod(true, x1))) A__ADD(s(prod(false, x1)), x2) -> c3(A__ADD(a__prod(false, mark(x1)), mark(x2)), MARK(prod(false, x1))) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__PROD_2, A__FACT_1 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c27_1, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1, c24_2, c25_2, c25_1, c26_2, c26_1, c_2, c_1 ---------------------------------------- (199) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (200) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) 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c3(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(s(z0))) -> c3(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(0)) -> c3(A__ADD(mark(x0), a__p(0)), MARK(x0)) A__ADD(s(x0), p(true)) -> c3(A__ADD(mark(x0), a__p(true)), MARK(x0)) A__ADD(s(x0), p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1)))) A__ADD(s(x0), add(x1, x2)) -> c3(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), add(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), add(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, p(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, s(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, 0)) -> c3(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), add(x1, true)) -> c3(A__ADD(mark(x0), a__add(mark(x1), true)), MARK(x0)) A__ADD(s(x0), add(x1, false)) -> c3(A__ADD(mark(x0), a__add(mark(x1), false)), MARK(x0)) A__ADD(s(x0), add(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), add(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(p(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(s(z0), x2)) -> c3(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(0, x2)) -> c3(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) A__ADD(s(x0), add(true, x2)) -> c3(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(x0)) A__ADD(s(x0), add(false, x2)) -> c3(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), add(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), add(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), add(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__add(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), add(x1, x2)) -> c3(A__ADD(0, a__add(mark(x1), mark(x2)))) A__ADD(s(x0), s(fact(z0))) -> c3(A__ADD(mark(x0), s(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), s(zero(z0))) -> c3(A__ADD(mark(x0), s(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(prod(z0, z1))) -> c3(A__ADD(mark(x0), s(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(p(z0))) -> c3(A__ADD(mark(x0), s(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(add(z0, z1))) -> c3(A__ADD(mark(x0), s(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(s(z0))) -> c3(A__ADD(mark(x0), s(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(0)) -> c3(A__ADD(mark(x0), s(0)), MARK(x0)) A__ADD(s(x0), s(true)) -> c3(A__ADD(mark(x0), s(true)), MARK(x0)) A__ADD(s(x0), s(false)) -> c3(A__ADD(mark(x0), s(false)), MARK(x0)) A__ADD(s(fact(z0)), s(x1)) -> c3(A__ADD(a__fact(mark(z0)), s(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), s(x1)) -> 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z1)), 0) -> c3(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) A__ADD(s(s(z0)), 0) -> c3(A__ADD(s(mark(z0)), 0), MARK(s(z0))) A__ADD(s(0), 0) -> c3(A__ADD(0, 0)) A__ADD(s(fact(z0)), true) -> c3(A__ADD(a__fact(mark(z0)), true), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), true) -> c3(A__ADD(a__if(mark(z0), z1, z2), true), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), true) -> c3(A__ADD(a__zero(mark(z0)), true), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), true) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), true), MARK(prod(z0, z1))) A__ADD(s(p(z0)), true) -> c3(A__ADD(a__p(mark(z0)), true), MARK(p(z0))) A__ADD(s(add(z0, z1)), true) -> c3(A__ADD(a__add(mark(z0), mark(z1)), true), MARK(add(z0, z1))) A__ADD(s(s(z0)), true) -> c3(A__ADD(s(mark(z0)), true), MARK(s(z0))) A__ADD(s(0), true) -> c3(A__ADD(0, true)) A__ADD(s(fact(z0)), false) -> c3(A__ADD(a__fact(mark(z0)), false), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), false) -> c3(A__ADD(a__if(mark(z0), z1, z2), false), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), false) -> c3(A__ADD(a__zero(mark(z0)), false), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), false) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), false), MARK(prod(z0, z1))) A__ADD(s(p(z0)), false) -> c3(A__ADD(a__p(mark(z0)), false), MARK(p(z0))) A__ADD(s(add(z0, z1)), false) -> c3(A__ADD(a__add(mark(z0), mark(z1)), false), MARK(add(z0, z1))) A__ADD(s(s(z0)), false) -> c3(A__ADD(s(mark(z0)), false), MARK(s(z0))) A__ADD(s(0), false) -> c3(A__ADD(0, false)) A__ADD(s(fact(x0)), x1) -> c3(A__ADD(a__if(a__zero(mark(mark(x0))), s(0), prod(mark(x0), fact(p(mark(x0))))), mark(x1)), MARK(fact(x0))) A__ADD(s(fact(fact(z0))), x1) -> c3(A__ADD(a__fact(a__fact(mark(z0))), mark(x1)), MARK(fact(fact(z0)))) A__ADD(s(fact(if(z0, z1, z2))), x1) -> c3(A__ADD(a__fact(a__if(mark(z0), z1, z2)), mark(x1)), MARK(fact(if(z0, z1, z2)))) A__ADD(s(fact(zero(z0))), x1) -> c3(A__ADD(a__fact(a__zero(mark(z0))), mark(x1)), MARK(fact(zero(z0)))) A__ADD(s(fact(prod(z0, z1))), x1) -> c3(A__ADD(a__fact(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(fact(prod(z0, z1)))) A__ADD(s(fact(p(z0))), x1) -> c3(A__ADD(a__fact(a__p(mark(z0))), mark(x1)), MARK(fact(p(z0)))) A__ADD(s(fact(add(z0, z1))), x1) -> c3(A__ADD(a__fact(a__add(mark(z0), mark(z1))), mark(x1)), MARK(fact(add(z0, z1)))) A__ADD(s(fact(s(z0))), x1) -> c3(A__ADD(a__fact(s(mark(z0))), mark(x1)), MARK(fact(s(z0)))) A__ADD(s(fact(0)), x1) -> c3(A__ADD(a__fact(0), mark(x1)), MARK(fact(0))) A__ADD(s(fact(true)), x1) -> c3(A__ADD(a__fact(true), mark(x1)), MARK(fact(true))) A__ADD(s(fact(false)), x1) -> c3(A__ADD(a__fact(false), mark(x1)), MARK(fact(false))) A__ADD(s(fact(x0)), x1) -> c3(MARK(fact(x0))) A__ADD(s(if(fact(z0), x1, x2)), x3) -> c3(A__ADD(a__if(a__fact(mark(z0)), x1, x2), mark(x3)), MARK(if(fact(z0), x1, x2))) A__ADD(s(if(if(z0, z1, z2), x1, x2)), x3) -> c3(A__ADD(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(if(if(z0, z1, z2), x1, x2))) A__ADD(s(if(zero(z0), x1, x2)), x3) -> c3(A__ADD(a__if(a__zero(mark(z0)), x1, x2), mark(x3)), MARK(if(zero(z0), x1, x2))) A__ADD(s(if(prod(z0, z1), x1, x2)), x3) -> c3(A__ADD(a__if(a__prod(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(prod(z0, z1), x1, x2))) A__ADD(s(if(p(z0), x1, x2)), x3) -> c3(A__ADD(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(if(p(z0), x1, x2))) A__ADD(s(if(add(z0, z1), x1, x2)), x3) -> c3(A__ADD(a__if(a__add(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(add(z0, z1), x1, x2))) A__ADD(s(if(s(z0), x1, x2)), x3) -> c3(A__ADD(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(if(s(z0), x1, x2))) A__ADD(s(if(true, x1, x2)), x3) -> c3(A__ADD(a__if(true, x1, x2), mark(x3)), MARK(if(true, x1, x2))) A__ADD(s(if(false, x1, x2)), x3) -> c3(A__ADD(a__if(false, x1, x2), mark(x3)), MARK(if(false, x1, x2))) A__ADD(s(if(x0, z1, z2)), x3) -> c3(MARK(if(x0, z1, z2))) A__ADD(s(if(0, x1, x2)), x3) -> c3(A__ADD(a__if(0, x1, x2), mark(x3))) A__ADD(s(zero(fact(z0))), x1) -> c3(A__ADD(a__zero(a__fact(mark(z0))), mark(x1)), MARK(zero(fact(z0)))) A__ADD(s(zero(if(z0, z1, z2))), x1) -> c3(A__ADD(a__zero(a__if(mark(z0), z1, z2)), mark(x1)), MARK(zero(if(z0, z1, z2)))) A__ADD(s(zero(zero(z0))), x1) -> c3(A__ADD(a__zero(a__zero(mark(z0))), mark(x1)), MARK(zero(zero(z0)))) A__ADD(s(zero(prod(z0, z1))), x1) -> c3(A__ADD(a__zero(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(zero(prod(z0, z1)))) A__ADD(s(zero(p(z0))), x1) -> c3(A__ADD(a__zero(a__p(mark(z0))), mark(x1)), MARK(zero(p(z0)))) A__ADD(s(zero(add(z0, z1))), x1) -> c3(A__ADD(a__zero(a__add(mark(z0), mark(z1))), mark(x1)), MARK(zero(add(z0, z1)))) A__ADD(s(zero(s(z0))), x1) -> c3(A__ADD(a__zero(s(mark(z0))), mark(x1)), MARK(zero(s(z0)))) A__ADD(s(zero(0)), x1) -> c3(A__ADD(a__zero(0), mark(x1)), MARK(zero(0))) A__ADD(s(zero(true)), x1) -> c3(A__ADD(a__zero(true), mark(x1)), MARK(zero(true))) A__ADD(s(zero(false)), x1) -> c3(A__ADD(a__zero(false), mark(x1)), MARK(zero(false))) A__ADD(s(zero(x0)), x1) -> c3(MARK(zero(x0))) A__ADD(s(prod(x0, fact(z0))), x2) -> c3(A__ADD(a__prod(mark(x0), a__fact(mark(z0))), mark(x2)), MARK(prod(x0, fact(z0)))) A__ADD(s(prod(x0, if(z0, z1, z2))), x2) -> c3(A__ADD(a__prod(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(prod(x0, if(z0, z1, z2)))) A__ADD(s(prod(x0, zero(z0))), x2) -> c3(A__ADD(a__prod(mark(x0), a__zero(mark(z0))), mark(x2)), MARK(prod(x0, zero(z0)))) A__ADD(s(prod(x0, prod(z0, z1))), x2) -> c3(A__ADD(a__prod(mark(x0), a__prod(mark(z0), mark(z1))), mark(x2)), MARK(prod(x0, prod(z0, z1)))) A__ADD(s(prod(x0, p(z0))), x2) -> c3(A__ADD(a__prod(mark(x0), a__p(mark(z0))), mark(x2)), MARK(prod(x0, p(z0)))) A__ADD(s(prod(x0, add(z0, z1))), x2) -> c3(A__ADD(a__prod(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(prod(x0, add(z0, z1)))) A__ADD(s(prod(x0, s(z0))), x2) -> c3(A__ADD(a__prod(mark(x0), s(mark(z0))), mark(x2)), MARK(prod(x0, s(z0)))) A__ADD(s(prod(x0, 0)), x2) -> c3(A__ADD(a__prod(mark(x0), 0), mark(x2)), MARK(prod(x0, 0))) A__ADD(s(prod(x0, true)), x2) -> c3(A__ADD(a__prod(mark(x0), true), mark(x2)), MARK(prod(x0, true))) A__ADD(s(prod(x0, false)), x2) -> c3(A__ADD(a__prod(mark(x0), false), mark(x2)), MARK(prod(x0, false))) A__ADD(s(prod(fact(z0), x1)), x2) -> c3(A__ADD(a__prod(a__fact(mark(z0)), mark(x1)), mark(x2)), MARK(prod(fact(z0), x1))) A__ADD(s(prod(if(z0, z1, z2), x1)), x2) -> c3(A__ADD(a__prod(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(prod(if(z0, z1, z2), x1))) A__ADD(s(prod(zero(z0), x1)), x2) -> c3(A__ADD(a__prod(a__zero(mark(z0)), mark(x1)), mark(x2)), MARK(prod(zero(z0), x1))) A__ADD(s(prod(prod(z0, z1), x1)), x2) -> c3(A__ADD(a__prod(a__prod(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(prod(prod(z0, z1), x1))) A__ADD(s(prod(p(z0), x1)), x2) -> c3(A__ADD(a__prod(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(prod(p(z0), x1))) A__ADD(s(prod(add(z0, z1), x1)), x2) -> c3(A__ADD(a__prod(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(prod(add(z0, z1), x1))) A__ADD(s(prod(s(z0), x1)), x2) -> c3(A__ADD(a__prod(s(mark(z0)), mark(x1)), mark(x2)), MARK(prod(s(z0), x1))) A__ADD(s(prod(0, x1)), x2) -> c3(A__ADD(a__prod(0, mark(x1)), mark(x2)), MARK(prod(0, x1))) A__ADD(s(prod(true, x1)), x2) -> c3(A__ADD(a__prod(true, mark(x1)), mark(x2)), MARK(prod(true, x1))) A__ADD(s(prod(false, x1)), x2) -> c3(A__ADD(a__prod(false, mark(x1)), mark(x2)), MARK(prod(false, x1))) A__ADD(s(prod(x0, x1)), x2) -> c3(MARK(prod(x0, x1))) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), 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p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1)))) A__ADD(s(x0), add(x1, x2)) -> c3(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), add(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), add(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, p(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, s(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, 0)) -> c3(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), add(x1, true)) -> c3(A__ADD(mark(x0), a__add(mark(x1), true)), MARK(x0)) A__ADD(s(x0), add(x1, false)) -> c3(A__ADD(mark(x0), a__add(mark(x1), false)), MARK(x0)) A__ADD(s(x0), add(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), add(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(p(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(s(z0), x2)) -> c3(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(0, x2)) -> c3(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) A__ADD(s(x0), add(true, x2)) -> c3(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(x0)) A__ADD(s(x0), add(false, x2)) -> c3(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), add(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), add(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), add(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__add(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), add(x1, x2)) -> c3(A__ADD(0, a__add(mark(x1), mark(x2)))) A__ADD(s(x0), s(fact(z0))) -> c3(A__ADD(mark(x0), s(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), s(zero(z0))) -> c3(A__ADD(mark(x0), s(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(prod(z0, z1))) -> c3(A__ADD(mark(x0), s(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(p(z0))) -> c3(A__ADD(mark(x0), s(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(add(z0, z1))) -> c3(A__ADD(mark(x0), s(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(s(z0))) -> c3(A__ADD(mark(x0), s(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(0)) -> c3(A__ADD(mark(x0), s(0)), MARK(x0)) A__ADD(s(x0), s(true)) -> c3(A__ADD(mark(x0), s(true)), MARK(x0)) A__ADD(s(x0), s(false)) -> c3(A__ADD(mark(x0), s(false)), MARK(x0)) A__ADD(s(fact(z0)), s(x1)) -> c3(A__ADD(a__fact(mark(z0)), s(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), s(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), s(x1)) -> c3(A__ADD(a__zero(mark(z0)), s(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), s(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), s(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), s(x1)) -> c3(A__ADD(a__p(mark(z0)), s(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), s(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), s(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), s(x1)) -> c3(A__ADD(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__ADD(s(0), s(x1)) -> c3(A__ADD(0, s(mark(x1)))) A__ADD(s(fact(z0)), 0) -> c3(A__ADD(a__fact(mark(z0)), 0), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), 0) -> c3(A__ADD(a__if(mark(z0), z1, z2), 0), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), 0) -> c3(A__ADD(a__zero(mark(z0)), 0), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), 0) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), 0), MARK(prod(z0, z1))) A__ADD(s(p(z0)), 0) -> c3(A__ADD(a__p(mark(z0)), 0), MARK(p(z0))) A__ADD(s(add(z0, z1)), 0) -> c3(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) A__ADD(s(s(z0)), 0) -> c3(A__ADD(s(mark(z0)), 0), MARK(s(z0))) A__ADD(s(0), 0) -> c3(A__ADD(0, 0)) A__ADD(s(fact(z0)), true) -> c3(A__ADD(a__fact(mark(z0)), true), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), true) -> c3(A__ADD(a__if(mark(z0), z1, z2), true), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), true) -> c3(A__ADD(a__zero(mark(z0)), true), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), true) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), true), MARK(prod(z0, z1))) A__ADD(s(p(z0)), true) -> c3(A__ADD(a__p(mark(z0)), true), MARK(p(z0))) A__ADD(s(add(z0, z1)), true) -> c3(A__ADD(a__add(mark(z0), mark(z1)), true), MARK(add(z0, z1))) A__ADD(s(s(z0)), true) -> c3(A__ADD(s(mark(z0)), true), MARK(s(z0))) A__ADD(s(0), true) -> c3(A__ADD(0, true)) A__ADD(s(fact(z0)), false) -> c3(A__ADD(a__fact(mark(z0)), false), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), false) -> c3(A__ADD(a__if(mark(z0), z1, z2), false), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), false) -> c3(A__ADD(a__zero(mark(z0)), false), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), false) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), false), MARK(prod(z0, z1))) A__ADD(s(p(z0)), false) -> c3(A__ADD(a__p(mark(z0)), false), MARK(p(z0))) A__ADD(s(add(z0, z1)), false) -> c3(A__ADD(a__add(mark(z0), mark(z1)), false), MARK(add(z0, z1))) A__ADD(s(s(z0)), false) -> c3(A__ADD(s(mark(z0)), false), MARK(s(z0))) A__ADD(s(0), false) -> c3(A__ADD(0, false)) A__ADD(s(fact(x0)), x1) -> c3(A__ADD(a__if(a__zero(mark(mark(x0))), s(0), prod(mark(x0), fact(p(mark(x0))))), mark(x1)), MARK(fact(x0))) A__ADD(s(fact(fact(z0))), x1) -> c3(A__ADD(a__fact(a__fact(mark(z0))), mark(x1)), MARK(fact(fact(z0)))) A__ADD(s(fact(if(z0, z1, z2))), x1) -> c3(A__ADD(a__fact(a__if(mark(z0), z1, z2)), mark(x1)), MARK(fact(if(z0, z1, z2)))) A__ADD(s(fact(zero(z0))), x1) -> c3(A__ADD(a__fact(a__zero(mark(z0))), mark(x1)), MARK(fact(zero(z0)))) A__ADD(s(fact(prod(z0, z1))), x1) -> c3(A__ADD(a__fact(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(fact(prod(z0, z1)))) A__ADD(s(fact(p(z0))), x1) -> c3(A__ADD(a__fact(a__p(mark(z0))), mark(x1)), MARK(fact(p(z0)))) A__ADD(s(fact(add(z0, z1))), x1) -> c3(A__ADD(a__fact(a__add(mark(z0), mark(z1))), mark(x1)), MARK(fact(add(z0, z1)))) A__ADD(s(fact(s(z0))), x1) -> c3(A__ADD(a__fact(s(mark(z0))), mark(x1)), MARK(fact(s(z0)))) A__ADD(s(fact(0)), x1) -> c3(A__ADD(a__fact(0), mark(x1)), MARK(fact(0))) A__ADD(s(fact(true)), x1) -> c3(A__ADD(a__fact(true), mark(x1)), MARK(fact(true))) A__ADD(s(fact(false)), x1) -> c3(A__ADD(a__fact(false), mark(x1)), MARK(fact(false))) A__ADD(s(fact(x0)), x1) -> c3(MARK(fact(x0))) A__ADD(s(if(fact(z0), x1, x2)), x3) -> c3(A__ADD(a__if(a__fact(mark(z0)), x1, x2), mark(x3)), MARK(if(fact(z0), x1, x2))) A__ADD(s(if(if(z0, z1, z2), x1, x2)), x3) -> c3(A__ADD(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(if(if(z0, z1, z2), x1, x2))) A__ADD(s(if(zero(z0), x1, x2)), x3) -> c3(A__ADD(a__if(a__zero(mark(z0)), x1, x2), mark(x3)), MARK(if(zero(z0), x1, x2))) A__ADD(s(if(prod(z0, z1), x1, x2)), x3) -> c3(A__ADD(a__if(a__prod(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(prod(z0, z1), x1, x2))) A__ADD(s(if(p(z0), x1, x2)), x3) -> c3(A__ADD(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(if(p(z0), x1, x2))) A__ADD(s(if(add(z0, z1), x1, x2)), x3) -> c3(A__ADD(a__if(a__add(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(add(z0, z1), x1, x2))) A__ADD(s(if(s(z0), x1, x2)), x3) -> c3(A__ADD(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(if(s(z0), x1, x2))) A__ADD(s(if(true, x1, x2)), x3) -> c3(A__ADD(a__if(true, x1, x2), mark(x3)), MARK(if(true, x1, x2))) A__ADD(s(if(false, x1, x2)), x3) -> c3(A__ADD(a__if(false, x1, x2), mark(x3)), MARK(if(false, x1, x2))) A__ADD(s(if(x0, z1, z2)), x3) -> c3(MARK(if(x0, z1, z2))) A__ADD(s(if(0, x1, x2)), x3) -> c3(A__ADD(a__if(0, x1, x2), mark(x3))) A__ADD(s(zero(fact(z0))), x1) -> c3(A__ADD(a__zero(a__fact(mark(z0))), mark(x1)), MARK(zero(fact(z0)))) A__ADD(s(zero(if(z0, z1, z2))), x1) -> c3(A__ADD(a__zero(a__if(mark(z0), z1, z2)), mark(x1)), MARK(zero(if(z0, z1, z2)))) A__ADD(s(zero(zero(z0))), x1) -> c3(A__ADD(a__zero(a__zero(mark(z0))), mark(x1)), MARK(zero(zero(z0)))) A__ADD(s(zero(prod(z0, z1))), x1) -> c3(A__ADD(a__zero(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(zero(prod(z0, z1)))) A__ADD(s(zero(p(z0))), x1) -> c3(A__ADD(a__zero(a__p(mark(z0))), mark(x1)), MARK(zero(p(z0)))) A__ADD(s(zero(add(z0, z1))), x1) -> c3(A__ADD(a__zero(a__add(mark(z0), mark(z1))), mark(x1)), MARK(zero(add(z0, z1)))) A__ADD(s(zero(s(z0))), x1) -> c3(A__ADD(a__zero(s(mark(z0))), mark(x1)), MARK(zero(s(z0)))) A__ADD(s(zero(0)), x1) -> c3(A__ADD(a__zero(0), mark(x1)), MARK(zero(0))) A__ADD(s(zero(true)), x1) -> c3(A__ADD(a__zero(true), mark(x1)), MARK(zero(true))) A__ADD(s(zero(false)), x1) -> c3(A__ADD(a__zero(false), mark(x1)), MARK(zero(false))) A__ADD(s(zero(x0)), x1) -> c3(MARK(zero(x0))) A__ADD(s(prod(x0, fact(z0))), x2) -> c3(A__ADD(a__prod(mark(x0), a__fact(mark(z0))), mark(x2)), MARK(prod(x0, fact(z0)))) A__ADD(s(prod(x0, if(z0, z1, z2))), x2) -> c3(A__ADD(a__prod(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(prod(x0, if(z0, z1, z2)))) A__ADD(s(prod(x0, zero(z0))), x2) -> c3(A__ADD(a__prod(mark(x0), a__zero(mark(z0))), mark(x2)), MARK(prod(x0, zero(z0)))) A__ADD(s(prod(x0, prod(z0, z1))), x2) -> c3(A__ADD(a__prod(mark(x0), a__prod(mark(z0), mark(z1))), mark(x2)), MARK(prod(x0, prod(z0, z1)))) A__ADD(s(prod(x0, p(z0))), x2) -> c3(A__ADD(a__prod(mark(x0), a__p(mark(z0))), mark(x2)), MARK(prod(x0, p(z0)))) A__ADD(s(prod(x0, add(z0, z1))), x2) -> c3(A__ADD(a__prod(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(prod(x0, add(z0, z1)))) A__ADD(s(prod(x0, s(z0))), x2) -> c3(A__ADD(a__prod(mark(x0), s(mark(z0))), mark(x2)), MARK(prod(x0, s(z0)))) A__ADD(s(prod(x0, 0)), x2) -> c3(A__ADD(a__prod(mark(x0), 0), mark(x2)), MARK(prod(x0, 0))) A__ADD(s(prod(x0, true)), x2) -> c3(A__ADD(a__prod(mark(x0), true), mark(x2)), MARK(prod(x0, true))) A__ADD(s(prod(x0, false)), x2) -> c3(A__ADD(a__prod(mark(x0), false), mark(x2)), MARK(prod(x0, false))) A__ADD(s(prod(fact(z0), x1)), x2) -> c3(A__ADD(a__prod(a__fact(mark(z0)), mark(x1)), mark(x2)), MARK(prod(fact(z0), x1))) A__ADD(s(prod(if(z0, z1, z2), x1)), x2) -> c3(A__ADD(a__prod(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(prod(if(z0, z1, z2), x1))) A__ADD(s(prod(zero(z0), x1)), x2) -> c3(A__ADD(a__prod(a__zero(mark(z0)), mark(x1)), mark(x2)), MARK(prod(zero(z0), x1))) A__ADD(s(prod(prod(z0, z1), x1)), x2) -> c3(A__ADD(a__prod(a__prod(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(prod(prod(z0, z1), x1))) A__ADD(s(prod(p(z0), x1)), x2) -> c3(A__ADD(a__prod(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(prod(p(z0), x1))) A__ADD(s(prod(add(z0, z1), x1)), x2) -> c3(A__ADD(a__prod(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(prod(add(z0, z1), x1))) A__ADD(s(prod(s(z0), x1)), x2) -> c3(A__ADD(a__prod(s(mark(z0)), mark(x1)), mark(x2)), MARK(prod(s(z0), x1))) A__ADD(s(prod(0, x1)), x2) -> c3(A__ADD(a__prod(0, mark(x1)), mark(x2)), MARK(prod(0, x1))) A__ADD(s(prod(true, x1)), x2) -> c3(A__ADD(a__prod(true, mark(x1)), mark(x2)), MARK(prod(true, x1))) A__ADD(s(prod(false, x1)), x2) -> c3(A__ADD(a__prod(false, mark(x1)), mark(x2)), MARK(prod(false, x1))) A__ADD(s(prod(x0, x1)), x2) -> c3(MARK(prod(x0, x1))) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__PROD_2, A__FACT_1 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c27_1, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1, c24_2, c25_2, c25_1, c26_2, c26_1, c_2, c_1 ---------------------------------------- (201) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__ADD(s(p(z0)), x1) -> c3(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) by A__ADD(s(p(x0)), fact(z0)) -> c3(A__ADD(a__p(mark(x0)), a__fact(mark(z0))), MARK(p(x0))) A__ADD(s(p(x0)), if(z0, z1, z2)) -> c3(A__ADD(a__p(mark(x0)), a__if(mark(z0), z1, z2)), MARK(p(x0))) A__ADD(s(p(x0)), zero(z0)) -> c3(A__ADD(a__p(mark(x0)), a__zero(mark(z0))), MARK(p(x0))) A__ADD(s(p(x0)), prod(z0, z1)) -> c3(A__ADD(a__p(mark(x0)), a__prod(mark(z0), mark(z1))), MARK(p(x0))) A__ADD(s(p(x0)), p(z0)) -> c3(A__ADD(a__p(mark(x0)), a__p(mark(z0))), MARK(p(x0))) A__ADD(s(p(x0)), add(z0, z1)) -> c3(A__ADD(a__p(mark(x0)), a__add(mark(z0), mark(z1))), MARK(p(x0))) A__ADD(s(p(x0)), s(z0)) -> c3(A__ADD(a__p(mark(x0)), s(mark(z0))), MARK(p(x0))) A__ADD(s(p(x0)), 0) -> c3(A__ADD(a__p(mark(x0)), 0), MARK(p(x0))) A__ADD(s(p(x0)), true) -> c3(A__ADD(a__p(mark(x0)), true), MARK(p(x0))) A__ADD(s(p(x0)), false) -> c3(A__ADD(a__p(mark(x0)), false), MARK(p(x0))) A__ADD(s(p(x0)), x1) -> c3(A__ADD(p(mark(x0)), mark(x1)), MARK(p(x0))) A__ADD(s(p(fact(z0))), x1) -> c3(A__ADD(a__p(a__fact(mark(z0))), mark(x1)), MARK(p(fact(z0)))) A__ADD(s(p(if(z0, z1, z2))), x1) -> c3(A__ADD(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2)))) A__ADD(s(p(zero(z0))), x1) -> c3(A__ADD(a__p(a__zero(mark(z0))), mark(x1)), MARK(p(zero(z0)))) A__ADD(s(p(prod(z0, z1))), x1) -> c3(A__ADD(a__p(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(p(prod(z0, z1)))) A__ADD(s(p(p(z0))), x1) -> c3(A__ADD(a__p(a__p(mark(z0))), mark(x1)), MARK(p(p(z0)))) A__ADD(s(p(add(z0, z1))), x1) -> c3(A__ADD(a__p(a__add(mark(z0), mark(z1))), mark(x1)), MARK(p(add(z0, z1)))) A__ADD(s(p(s(z0))), x1) -> c3(A__ADD(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0)))) A__ADD(s(p(0)), x1) -> c3(A__ADD(a__p(0), mark(x1)), MARK(p(0))) A__ADD(s(p(true)), x1) -> c3(A__ADD(a__p(true), mark(x1)), MARK(p(true))) A__ADD(s(p(false)), x1) -> c3(A__ADD(a__p(false), mark(x1)), MARK(p(false))) ---------------------------------------- (202) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1)))) A__ADD(s(x0), prod(x1, x2)) -> c3(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), prod(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, p(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, s(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, 0)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), prod(x1, true)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(x0)) A__ADD(s(x0), prod(x1, false)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(x0)) A__ADD(s(x0), prod(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(p(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(0, x2)) -> c3(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(true, x2)) -> c3(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(false, x2)) -> c3(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), prod(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2)))) A__ADD(s(x0), p(x1)) -> c3(A__ADD(mark(x0), p(mark(x1))), MARK(x0)) A__ADD(s(x0), p(fact(z0))) -> c3(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), p(zero(z0))) -> c3(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(p(z0))) -> c3(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(add(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(s(z0))) -> c3(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(0)) -> c3(A__ADD(mark(x0), a__p(0)), MARK(x0)) A__ADD(s(x0), p(true)) -> c3(A__ADD(mark(x0), a__p(true)), MARK(x0)) A__ADD(s(x0), p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1)))) A__ADD(s(x0), add(x1, x2)) -> c3(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), add(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), add(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, p(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, s(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, 0)) -> c3(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), add(x1, true)) -> c3(A__ADD(mark(x0), a__add(mark(x1), true)), MARK(x0)) A__ADD(s(x0), add(x1, false)) -> c3(A__ADD(mark(x0), a__add(mark(x1), false)), MARK(x0)) A__ADD(s(x0), add(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), add(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(p(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(s(z0), x2)) -> c3(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(0, x2)) -> c3(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) A__ADD(s(x0), add(true, x2)) -> c3(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(x0)) A__ADD(s(x0), add(false, x2)) -> c3(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), add(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), add(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), add(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__add(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), add(x1, x2)) -> c3(A__ADD(0, a__add(mark(x1), mark(x2)))) A__ADD(s(x0), s(fact(z0))) -> c3(A__ADD(mark(x0), s(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), s(zero(z0))) -> c3(A__ADD(mark(x0), s(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(prod(z0, z1))) -> c3(A__ADD(mark(x0), s(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(p(z0))) -> c3(A__ADD(mark(x0), s(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(add(z0, z1))) -> c3(A__ADD(mark(x0), s(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(s(z0))) -> c3(A__ADD(mark(x0), s(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(0)) -> c3(A__ADD(mark(x0), s(0)), MARK(x0)) A__ADD(s(x0), s(true)) -> c3(A__ADD(mark(x0), s(true)), MARK(x0)) A__ADD(s(x0), s(false)) -> c3(A__ADD(mark(x0), s(false)), MARK(x0)) A__ADD(s(fact(z0)), s(x1)) -> c3(A__ADD(a__fact(mark(z0)), s(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), s(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), s(x1)) -> c3(A__ADD(a__zero(mark(z0)), s(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), s(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), s(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), s(x1)) -> c3(A__ADD(a__p(mark(z0)), s(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), s(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), s(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), s(x1)) -> c3(A__ADD(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__ADD(s(0), s(x1)) -> c3(A__ADD(0, s(mark(x1)))) A__ADD(s(fact(z0)), 0) -> c3(A__ADD(a__fact(mark(z0)), 0), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), 0) -> c3(A__ADD(a__if(mark(z0), z1, z2), 0), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), 0) -> c3(A__ADD(a__zero(mark(z0)), 0), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), 0) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), 0), MARK(prod(z0, z1))) A__ADD(s(p(z0)), 0) -> c3(A__ADD(a__p(mark(z0)), 0), MARK(p(z0))) A__ADD(s(add(z0, z1)), 0) -> c3(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) A__ADD(s(s(z0)), 0) -> c3(A__ADD(s(mark(z0)), 0), MARK(s(z0))) A__ADD(s(0), 0) -> c3(A__ADD(0, 0)) A__ADD(s(fact(z0)), true) -> c3(A__ADD(a__fact(mark(z0)), true), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), true) -> c3(A__ADD(a__if(mark(z0), z1, z2), true), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), true) -> c3(A__ADD(a__zero(mark(z0)), true), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), true) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), true), MARK(prod(z0, z1))) A__ADD(s(p(z0)), true) -> c3(A__ADD(a__p(mark(z0)), true), MARK(p(z0))) A__ADD(s(add(z0, z1)), true) -> c3(A__ADD(a__add(mark(z0), mark(z1)), true), MARK(add(z0, z1))) A__ADD(s(s(z0)), true) -> c3(A__ADD(s(mark(z0)), true), MARK(s(z0))) A__ADD(s(0), true) -> c3(A__ADD(0, true)) A__ADD(s(fact(z0)), false) -> c3(A__ADD(a__fact(mark(z0)), false), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), false) -> c3(A__ADD(a__if(mark(z0), z1, z2), false), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), false) -> c3(A__ADD(a__zero(mark(z0)), false), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), false) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), false), MARK(prod(z0, z1))) A__ADD(s(p(z0)), false) -> c3(A__ADD(a__p(mark(z0)), false), MARK(p(z0))) A__ADD(s(add(z0, z1)), false) -> c3(A__ADD(a__add(mark(z0), mark(z1)), false), MARK(add(z0, z1))) A__ADD(s(s(z0)), false) -> c3(A__ADD(s(mark(z0)), false), MARK(s(z0))) A__ADD(s(0), false) -> c3(A__ADD(0, false)) A__ADD(s(fact(x0)), x1) -> c3(A__ADD(a__if(a__zero(mark(mark(x0))), s(0), prod(mark(x0), fact(p(mark(x0))))), mark(x1)), MARK(fact(x0))) A__ADD(s(fact(fact(z0))), x1) -> c3(A__ADD(a__fact(a__fact(mark(z0))), mark(x1)), MARK(fact(fact(z0)))) A__ADD(s(fact(if(z0, z1, z2))), x1) -> c3(A__ADD(a__fact(a__if(mark(z0), z1, z2)), mark(x1)), MARK(fact(if(z0, z1, z2)))) A__ADD(s(fact(zero(z0))), x1) -> c3(A__ADD(a__fact(a__zero(mark(z0))), mark(x1)), MARK(fact(zero(z0)))) A__ADD(s(fact(prod(z0, z1))), x1) -> c3(A__ADD(a__fact(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(fact(prod(z0, z1)))) A__ADD(s(fact(p(z0))), x1) -> c3(A__ADD(a__fact(a__p(mark(z0))), mark(x1)), MARK(fact(p(z0)))) A__ADD(s(fact(add(z0, z1))), x1) -> c3(A__ADD(a__fact(a__add(mark(z0), mark(z1))), mark(x1)), MARK(fact(add(z0, z1)))) A__ADD(s(fact(s(z0))), x1) -> c3(A__ADD(a__fact(s(mark(z0))), mark(x1)), MARK(fact(s(z0)))) A__ADD(s(fact(0)), x1) -> c3(A__ADD(a__fact(0), mark(x1)), MARK(fact(0))) A__ADD(s(fact(true)), x1) -> c3(A__ADD(a__fact(true), mark(x1)), MARK(fact(true))) A__ADD(s(fact(false)), x1) -> c3(A__ADD(a__fact(false), mark(x1)), MARK(fact(false))) A__ADD(s(fact(x0)), x1) -> c3(MARK(fact(x0))) A__ADD(s(if(fact(z0), x1, x2)), x3) -> c3(A__ADD(a__if(a__fact(mark(z0)), x1, x2), mark(x3)), MARK(if(fact(z0), x1, x2))) A__ADD(s(if(if(z0, z1, z2), x1, x2)), x3) -> c3(A__ADD(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(if(if(z0, z1, z2), x1, x2))) A__ADD(s(if(zero(z0), x1, x2)), x3) -> c3(A__ADD(a__if(a__zero(mark(z0)), x1, x2), mark(x3)), MARK(if(zero(z0), x1, x2))) A__ADD(s(if(prod(z0, z1), x1, x2)), x3) -> c3(A__ADD(a__if(a__prod(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(prod(z0, z1), x1, x2))) A__ADD(s(if(p(z0), x1, x2)), x3) -> c3(A__ADD(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(if(p(z0), x1, x2))) A__ADD(s(if(add(z0, z1), x1, x2)), x3) -> c3(A__ADD(a__if(a__add(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(add(z0, z1), x1, x2))) A__ADD(s(if(s(z0), x1, x2)), x3) -> c3(A__ADD(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(if(s(z0), x1, x2))) A__ADD(s(if(true, x1, x2)), x3) -> c3(A__ADD(a__if(true, x1, x2), mark(x3)), MARK(if(true, x1, x2))) A__ADD(s(if(false, x1, x2)), x3) -> c3(A__ADD(a__if(false, x1, x2), mark(x3)), MARK(if(false, x1, x2))) A__ADD(s(if(x0, z1, z2)), x3) -> c3(MARK(if(x0, z1, z2))) A__ADD(s(if(0, x1, x2)), x3) -> c3(A__ADD(a__if(0, x1, x2), mark(x3))) A__ADD(s(zero(fact(z0))), x1) -> c3(A__ADD(a__zero(a__fact(mark(z0))), mark(x1)), MARK(zero(fact(z0)))) A__ADD(s(zero(if(z0, z1, z2))), x1) -> c3(A__ADD(a__zero(a__if(mark(z0), z1, z2)), mark(x1)), MARK(zero(if(z0, z1, z2)))) A__ADD(s(zero(zero(z0))), x1) -> c3(A__ADD(a__zero(a__zero(mark(z0))), mark(x1)), MARK(zero(zero(z0)))) A__ADD(s(zero(prod(z0, z1))), x1) -> c3(A__ADD(a__zero(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(zero(prod(z0, z1)))) A__ADD(s(zero(p(z0))), x1) -> c3(A__ADD(a__zero(a__p(mark(z0))), mark(x1)), MARK(zero(p(z0)))) A__ADD(s(zero(add(z0, z1))), x1) -> c3(A__ADD(a__zero(a__add(mark(z0), mark(z1))), mark(x1)), MARK(zero(add(z0, z1)))) A__ADD(s(zero(s(z0))), x1) -> c3(A__ADD(a__zero(s(mark(z0))), mark(x1)), MARK(zero(s(z0)))) A__ADD(s(zero(0)), x1) -> c3(A__ADD(a__zero(0), mark(x1)), MARK(zero(0))) A__ADD(s(zero(true)), x1) -> c3(A__ADD(a__zero(true), mark(x1)), MARK(zero(true))) A__ADD(s(zero(false)), x1) -> c3(A__ADD(a__zero(false), mark(x1)), MARK(zero(false))) A__ADD(s(zero(x0)), x1) -> c3(MARK(zero(x0))) A__ADD(s(prod(x0, fact(z0))), x2) -> c3(A__ADD(a__prod(mark(x0), a__fact(mark(z0))), mark(x2)), MARK(prod(x0, fact(z0)))) A__ADD(s(prod(x0, if(z0, z1, z2))), x2) -> c3(A__ADD(a__prod(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(prod(x0, if(z0, z1, z2)))) A__ADD(s(prod(x0, zero(z0))), x2) -> c3(A__ADD(a__prod(mark(x0), a__zero(mark(z0))), mark(x2)), MARK(prod(x0, zero(z0)))) A__ADD(s(prod(x0, prod(z0, z1))), x2) -> c3(A__ADD(a__prod(mark(x0), a__prod(mark(z0), mark(z1))), mark(x2)), MARK(prod(x0, prod(z0, z1)))) A__ADD(s(prod(x0, p(z0))), x2) -> c3(A__ADD(a__prod(mark(x0), a__p(mark(z0))), mark(x2)), MARK(prod(x0, p(z0)))) A__ADD(s(prod(x0, add(z0, z1))), x2) -> c3(A__ADD(a__prod(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(prod(x0, add(z0, z1)))) A__ADD(s(prod(x0, s(z0))), x2) -> c3(A__ADD(a__prod(mark(x0), s(mark(z0))), mark(x2)), MARK(prod(x0, s(z0)))) A__ADD(s(prod(x0, 0)), x2) -> c3(A__ADD(a__prod(mark(x0), 0), mark(x2)), MARK(prod(x0, 0))) A__ADD(s(prod(x0, true)), x2) -> c3(A__ADD(a__prod(mark(x0), true), mark(x2)), MARK(prod(x0, true))) A__ADD(s(prod(x0, false)), x2) -> c3(A__ADD(a__prod(mark(x0), false), mark(x2)), MARK(prod(x0, false))) A__ADD(s(prod(fact(z0), x1)), x2) -> c3(A__ADD(a__prod(a__fact(mark(z0)), mark(x1)), mark(x2)), MARK(prod(fact(z0), x1))) A__ADD(s(prod(if(z0, z1, z2), x1)), x2) -> c3(A__ADD(a__prod(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(prod(if(z0, z1, z2), x1))) A__ADD(s(prod(zero(z0), x1)), x2) -> c3(A__ADD(a__prod(a__zero(mark(z0)), mark(x1)), mark(x2)), MARK(prod(zero(z0), x1))) A__ADD(s(prod(prod(z0, z1), x1)), x2) -> c3(A__ADD(a__prod(a__prod(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(prod(prod(z0, z1), x1))) A__ADD(s(prod(p(z0), x1)), x2) -> c3(A__ADD(a__prod(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(prod(p(z0), x1))) A__ADD(s(prod(add(z0, z1), x1)), x2) -> c3(A__ADD(a__prod(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(prod(add(z0, z1), x1))) A__ADD(s(prod(s(z0), x1)), x2) -> c3(A__ADD(a__prod(s(mark(z0)), mark(x1)), mark(x2)), MARK(prod(s(z0), x1))) A__ADD(s(prod(0, x1)), x2) -> c3(A__ADD(a__prod(0, mark(x1)), mark(x2)), MARK(prod(0, x1))) A__ADD(s(prod(true, x1)), x2) -> c3(A__ADD(a__prod(true, mark(x1)), mark(x2)), MARK(prod(true, x1))) A__ADD(s(prod(false, x1)), x2) -> c3(A__ADD(a__prod(false, mark(x1)), mark(x2)), MARK(prod(false, x1))) A__ADD(s(prod(x0, x1)), x2) -> c3(MARK(prod(x0, x1))) A__ADD(s(p(x0)), x1) -> c3(A__ADD(p(mark(x0)), mark(x1)), MARK(p(x0))) A__ADD(s(p(fact(z0))), x1) -> c3(A__ADD(a__p(a__fact(mark(z0))), mark(x1)), MARK(p(fact(z0)))) A__ADD(s(p(if(z0, z1, z2))), x1) -> c3(A__ADD(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2)))) A__ADD(s(p(zero(z0))), x1) -> c3(A__ADD(a__p(a__zero(mark(z0))), mark(x1)), MARK(p(zero(z0)))) A__ADD(s(p(prod(z0, z1))), x1) -> c3(A__ADD(a__p(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(p(prod(z0, z1)))) A__ADD(s(p(p(z0))), x1) -> c3(A__ADD(a__p(a__p(mark(z0))), mark(x1)), MARK(p(p(z0)))) A__ADD(s(p(add(z0, z1))), x1) -> c3(A__ADD(a__p(a__add(mark(z0), mark(z1))), mark(x1)), MARK(p(add(z0, z1)))) A__ADD(s(p(s(z0))), x1) -> c3(A__ADD(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0)))) A__ADD(s(p(0)), x1) -> c3(A__ADD(a__p(0), mark(x1)), MARK(p(0))) A__ADD(s(p(true)), x1) -> c3(A__ADD(a__p(true), mark(x1)), MARK(p(true))) A__ADD(s(p(false)), x1) -> c3(A__ADD(a__p(false), mark(x1)), MARK(p(false))) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), 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A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), 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A__ADD(s(zero(0)), x1) -> c3(A__ADD(a__zero(0), mark(x1)), MARK(zero(0))) A__ADD(s(zero(true)), x1) -> c3(A__ADD(a__zero(true), mark(x1)), MARK(zero(true))) A__ADD(s(zero(false)), x1) -> c3(A__ADD(a__zero(false), mark(x1)), MARK(zero(false))) A__ADD(s(zero(x0)), x1) -> c3(MARK(zero(x0))) A__ADD(s(prod(x0, fact(z0))), x2) -> c3(A__ADD(a__prod(mark(x0), a__fact(mark(z0))), mark(x2)), MARK(prod(x0, fact(z0)))) A__ADD(s(prod(x0, if(z0, z1, z2))), x2) -> c3(A__ADD(a__prod(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(prod(x0, if(z0, z1, z2)))) A__ADD(s(prod(x0, zero(z0))), x2) -> c3(A__ADD(a__prod(mark(x0), a__zero(mark(z0))), mark(x2)), MARK(prod(x0, zero(z0)))) A__ADD(s(prod(x0, prod(z0, z1))), x2) -> c3(A__ADD(a__prod(mark(x0), a__prod(mark(z0), mark(z1))), mark(x2)), MARK(prod(x0, prod(z0, z1)))) A__ADD(s(prod(x0, p(z0))), x2) -> c3(A__ADD(a__prod(mark(x0), a__p(mark(z0))), mark(x2)), MARK(prod(x0, p(z0)))) A__ADD(s(prod(x0, add(z0, z1))), x2) -> c3(A__ADD(a__prod(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(prod(x0, add(z0, z1)))) A__ADD(s(prod(x0, s(z0))), x2) -> c3(A__ADD(a__prod(mark(x0), s(mark(z0))), mark(x2)), MARK(prod(x0, s(z0)))) A__ADD(s(prod(x0, 0)), x2) -> c3(A__ADD(a__prod(mark(x0), 0), mark(x2)), MARK(prod(x0, 0))) A__ADD(s(prod(x0, true)), x2) -> c3(A__ADD(a__prod(mark(x0), true), mark(x2)), MARK(prod(x0, true))) A__ADD(s(prod(x0, false)), x2) -> c3(A__ADD(a__prod(mark(x0), false), mark(x2)), MARK(prod(x0, false))) A__ADD(s(prod(fact(z0), x1)), x2) -> c3(A__ADD(a__prod(a__fact(mark(z0)), mark(x1)), mark(x2)), MARK(prod(fact(z0), x1))) A__ADD(s(prod(if(z0, z1, z2), x1)), x2) -> c3(A__ADD(a__prod(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(prod(if(z0, z1, z2), x1))) A__ADD(s(prod(zero(z0), x1)), x2) -> c3(A__ADD(a__prod(a__zero(mark(z0)), mark(x1)), mark(x2)), MARK(prod(zero(z0), x1))) A__ADD(s(prod(prod(z0, z1), x1)), x2) -> c3(A__ADD(a__prod(a__prod(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(prod(prod(z0, z1), x1))) A__ADD(s(prod(p(z0), x1)), x2) -> c3(A__ADD(a__prod(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(prod(p(z0), x1))) A__ADD(s(prod(add(z0, z1), x1)), x2) -> c3(A__ADD(a__prod(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(prod(add(z0, z1), x1))) A__ADD(s(prod(s(z0), x1)), x2) -> c3(A__ADD(a__prod(s(mark(z0)), mark(x1)), mark(x2)), MARK(prod(s(z0), x1))) A__ADD(s(prod(0, x1)), x2) -> c3(A__ADD(a__prod(0, mark(x1)), mark(x2)), MARK(prod(0, x1))) A__ADD(s(prod(true, x1)), x2) -> c3(A__ADD(a__prod(true, mark(x1)), mark(x2)), MARK(prod(true, x1))) A__ADD(s(prod(false, x1)), x2) -> c3(A__ADD(a__prod(false, mark(x1)), mark(x2)), MARK(prod(false, x1))) A__ADD(s(prod(x0, x1)), x2) -> c3(MARK(prod(x0, x1))) A__ADD(s(p(x0)), x1) -> c3(A__ADD(p(mark(x0)), mark(x1)), MARK(p(x0))) A__ADD(s(p(fact(z0))), x1) -> c3(A__ADD(a__p(a__fact(mark(z0))), mark(x1)), MARK(p(fact(z0)))) A__ADD(s(p(if(z0, z1, z2))), x1) -> c3(A__ADD(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2)))) A__ADD(s(p(zero(z0))), x1) -> c3(A__ADD(a__p(a__zero(mark(z0))), mark(x1)), MARK(p(zero(z0)))) A__ADD(s(p(prod(z0, z1))), x1) -> c3(A__ADD(a__p(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(p(prod(z0, z1)))) A__ADD(s(p(p(z0))), x1) -> c3(A__ADD(a__p(a__p(mark(z0))), mark(x1)), MARK(p(p(z0)))) A__ADD(s(p(add(z0, z1))), x1) -> c3(A__ADD(a__p(a__add(mark(z0), mark(z1))), mark(x1)), MARK(p(add(z0, z1)))) A__ADD(s(p(s(z0))), x1) -> c3(A__ADD(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0)))) A__ADD(s(p(0)), x1) -> c3(A__ADD(a__p(0), mark(x1)), MARK(p(0))) A__ADD(s(p(true)), x1) -> c3(A__ADD(a__p(true), mark(x1)), MARK(p(true))) A__ADD(s(p(false)), x1) -> c3(A__ADD(a__p(false), mark(x1)), MARK(p(false))) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__PROD_2, A__FACT_1 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c27_1, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1, c24_2, c25_2, c25_1, c26_2, c26_1, c_2, c_1 ---------------------------------------- (203) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (204) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1)))) A__ADD(s(x0), prod(x1, x2)) -> c3(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), prod(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, p(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, s(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, 0)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), prod(x1, true)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(x0)) A__ADD(s(x0), prod(x1, false)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(x0)) A__ADD(s(x0), prod(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(p(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(0, x2)) -> c3(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(true, x2)) -> c3(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(false, x2)) -> c3(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), prod(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2)))) A__ADD(s(x0), p(x1)) -> c3(A__ADD(mark(x0), p(mark(x1))), MARK(x0)) A__ADD(s(x0), p(fact(z0))) -> c3(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), p(zero(z0))) -> c3(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(p(z0))) -> c3(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(add(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(s(z0))) -> c3(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(0)) -> c3(A__ADD(mark(x0), a__p(0)), MARK(x0)) A__ADD(s(x0), p(true)) -> c3(A__ADD(mark(x0), a__p(true)), MARK(x0)) A__ADD(s(x0), p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1)))) A__ADD(s(x0), add(x1, x2)) -> c3(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), add(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), add(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, p(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, s(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, 0)) -> c3(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), add(x1, true)) -> c3(A__ADD(mark(x0), a__add(mark(x1), true)), MARK(x0)) A__ADD(s(x0), add(x1, false)) -> c3(A__ADD(mark(x0), a__add(mark(x1), false)), MARK(x0)) A__ADD(s(x0), add(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), add(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(p(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(s(z0), x2)) -> c3(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(0, x2)) -> c3(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) A__ADD(s(x0), add(true, x2)) -> c3(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(x0)) A__ADD(s(x0), add(false, x2)) -> c3(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), add(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), add(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), add(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__add(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), add(x1, x2)) -> c3(A__ADD(0, a__add(mark(x1), mark(x2)))) A__ADD(s(x0), s(fact(z0))) -> c3(A__ADD(mark(x0), s(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), s(zero(z0))) -> c3(A__ADD(mark(x0), s(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(prod(z0, z1))) -> c3(A__ADD(mark(x0), s(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(p(z0))) -> c3(A__ADD(mark(x0), s(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(add(z0, z1))) -> c3(A__ADD(mark(x0), s(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(s(z0))) -> c3(A__ADD(mark(x0), s(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(0)) -> c3(A__ADD(mark(x0), s(0)), MARK(x0)) A__ADD(s(x0), s(true)) -> c3(A__ADD(mark(x0), s(true)), MARK(x0)) A__ADD(s(x0), s(false)) -> c3(A__ADD(mark(x0), s(false)), MARK(x0)) A__ADD(s(fact(z0)), s(x1)) -> c3(A__ADD(a__fact(mark(z0)), s(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), s(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), s(x1)) -> c3(A__ADD(a__zero(mark(z0)), s(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), s(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), s(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), s(x1)) -> c3(A__ADD(a__p(mark(z0)), s(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), s(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), s(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), s(x1)) -> c3(A__ADD(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__ADD(s(0), s(x1)) -> c3(A__ADD(0, s(mark(x1)))) A__ADD(s(fact(z0)), 0) -> c3(A__ADD(a__fact(mark(z0)), 0), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), 0) -> c3(A__ADD(a__if(mark(z0), z1, z2), 0), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), 0) -> c3(A__ADD(a__zero(mark(z0)), 0), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), 0) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), 0), MARK(prod(z0, z1))) A__ADD(s(p(z0)), 0) -> c3(A__ADD(a__p(mark(z0)), 0), MARK(p(z0))) A__ADD(s(add(z0, z1)), 0) -> c3(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) A__ADD(s(s(z0)), 0) -> c3(A__ADD(s(mark(z0)), 0), MARK(s(z0))) A__ADD(s(0), 0) -> c3(A__ADD(0, 0)) A__ADD(s(fact(z0)), true) -> c3(A__ADD(a__fact(mark(z0)), true), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), true) -> c3(A__ADD(a__if(mark(z0), z1, z2), true), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), true) -> c3(A__ADD(a__zero(mark(z0)), true), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), true) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), true), MARK(prod(z0, z1))) A__ADD(s(p(z0)), true) -> c3(A__ADD(a__p(mark(z0)), true), MARK(p(z0))) A__ADD(s(add(z0, z1)), true) -> c3(A__ADD(a__add(mark(z0), mark(z1)), true), MARK(add(z0, z1))) A__ADD(s(s(z0)), true) -> c3(A__ADD(s(mark(z0)), true), MARK(s(z0))) A__ADD(s(0), true) -> c3(A__ADD(0, true)) A__ADD(s(fact(z0)), false) -> c3(A__ADD(a__fact(mark(z0)), false), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), false) -> c3(A__ADD(a__if(mark(z0), z1, z2), false), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), false) -> c3(A__ADD(a__zero(mark(z0)), false), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), false) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), false), MARK(prod(z0, z1))) A__ADD(s(p(z0)), false) -> c3(A__ADD(a__p(mark(z0)), false), MARK(p(z0))) A__ADD(s(add(z0, z1)), false) -> c3(A__ADD(a__add(mark(z0), mark(z1)), false), MARK(add(z0, z1))) A__ADD(s(s(z0)), false) -> c3(A__ADD(s(mark(z0)), false), MARK(s(z0))) A__ADD(s(0), false) -> c3(A__ADD(0, false)) A__ADD(s(fact(x0)), x1) -> c3(A__ADD(a__if(a__zero(mark(mark(x0))), s(0), prod(mark(x0), fact(p(mark(x0))))), mark(x1)), MARK(fact(x0))) A__ADD(s(fact(fact(z0))), x1) -> c3(A__ADD(a__fact(a__fact(mark(z0))), mark(x1)), MARK(fact(fact(z0)))) A__ADD(s(fact(if(z0, z1, z2))), x1) -> c3(A__ADD(a__fact(a__if(mark(z0), z1, z2)), mark(x1)), MARK(fact(if(z0, z1, z2)))) A__ADD(s(fact(zero(z0))), x1) -> c3(A__ADD(a__fact(a__zero(mark(z0))), mark(x1)), MARK(fact(zero(z0)))) A__ADD(s(fact(prod(z0, z1))), x1) -> c3(A__ADD(a__fact(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(fact(prod(z0, z1)))) A__ADD(s(fact(p(z0))), x1) -> c3(A__ADD(a__fact(a__p(mark(z0))), mark(x1)), MARK(fact(p(z0)))) A__ADD(s(fact(add(z0, z1))), x1) -> c3(A__ADD(a__fact(a__add(mark(z0), mark(z1))), mark(x1)), MARK(fact(add(z0, z1)))) A__ADD(s(fact(s(z0))), x1) -> c3(A__ADD(a__fact(s(mark(z0))), mark(x1)), MARK(fact(s(z0)))) A__ADD(s(fact(0)), x1) -> c3(A__ADD(a__fact(0), mark(x1)), MARK(fact(0))) A__ADD(s(fact(true)), x1) -> c3(A__ADD(a__fact(true), mark(x1)), MARK(fact(true))) A__ADD(s(fact(false)), x1) -> c3(A__ADD(a__fact(false), mark(x1)), MARK(fact(false))) A__ADD(s(fact(x0)), x1) -> c3(MARK(fact(x0))) A__ADD(s(if(fact(z0), x1, x2)), x3) -> c3(A__ADD(a__if(a__fact(mark(z0)), x1, x2), mark(x3)), MARK(if(fact(z0), x1, x2))) A__ADD(s(if(if(z0, z1, z2), x1, x2)), x3) -> c3(A__ADD(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(if(if(z0, z1, z2), x1, x2))) A__ADD(s(if(zero(z0), x1, x2)), x3) -> c3(A__ADD(a__if(a__zero(mark(z0)), x1, x2), mark(x3)), MARK(if(zero(z0), x1, x2))) A__ADD(s(if(prod(z0, z1), x1, x2)), x3) -> c3(A__ADD(a__if(a__prod(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(prod(z0, z1), x1, x2))) A__ADD(s(if(p(z0), x1, x2)), x3) -> c3(A__ADD(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(if(p(z0), x1, x2))) A__ADD(s(if(add(z0, z1), x1, x2)), x3) -> c3(A__ADD(a__if(a__add(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(add(z0, z1), x1, x2))) A__ADD(s(if(s(z0), x1, x2)), x3) -> c3(A__ADD(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(if(s(z0), x1, x2))) A__ADD(s(if(true, x1, x2)), x3) -> c3(A__ADD(a__if(true, x1, x2), mark(x3)), MARK(if(true, x1, x2))) A__ADD(s(if(false, x1, x2)), x3) -> c3(A__ADD(a__if(false, x1, x2), mark(x3)), MARK(if(false, x1, x2))) A__ADD(s(if(x0, z1, z2)), x3) -> c3(MARK(if(x0, z1, z2))) A__ADD(s(if(0, x1, x2)), x3) -> c3(A__ADD(a__if(0, x1, x2), mark(x3))) A__ADD(s(zero(fact(z0))), x1) -> c3(A__ADD(a__zero(a__fact(mark(z0))), mark(x1)), MARK(zero(fact(z0)))) A__ADD(s(zero(if(z0, z1, z2))), x1) -> c3(A__ADD(a__zero(a__if(mark(z0), z1, z2)), mark(x1)), MARK(zero(if(z0, z1, z2)))) A__ADD(s(zero(zero(z0))), x1) -> c3(A__ADD(a__zero(a__zero(mark(z0))), mark(x1)), MARK(zero(zero(z0)))) A__ADD(s(zero(prod(z0, z1))), x1) -> c3(A__ADD(a__zero(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(zero(prod(z0, z1)))) A__ADD(s(zero(p(z0))), x1) -> c3(A__ADD(a__zero(a__p(mark(z0))), mark(x1)), MARK(zero(p(z0)))) A__ADD(s(zero(add(z0, z1))), x1) -> c3(A__ADD(a__zero(a__add(mark(z0), mark(z1))), mark(x1)), MARK(zero(add(z0, z1)))) A__ADD(s(zero(s(z0))), x1) -> c3(A__ADD(a__zero(s(mark(z0))), mark(x1)), MARK(zero(s(z0)))) A__ADD(s(zero(0)), x1) -> c3(A__ADD(a__zero(0), mark(x1)), MARK(zero(0))) A__ADD(s(zero(true)), x1) -> c3(A__ADD(a__zero(true), mark(x1)), MARK(zero(true))) A__ADD(s(zero(false)), x1) -> c3(A__ADD(a__zero(false), mark(x1)), MARK(zero(false))) A__ADD(s(zero(x0)), x1) -> c3(MARK(zero(x0))) A__ADD(s(prod(x0, fact(z0))), x2) -> c3(A__ADD(a__prod(mark(x0), a__fact(mark(z0))), mark(x2)), MARK(prod(x0, fact(z0)))) A__ADD(s(prod(x0, if(z0, z1, z2))), x2) -> c3(A__ADD(a__prod(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(prod(x0, if(z0, z1, z2)))) A__ADD(s(prod(x0, zero(z0))), x2) -> c3(A__ADD(a__prod(mark(x0), a__zero(mark(z0))), mark(x2)), MARK(prod(x0, zero(z0)))) A__ADD(s(prod(x0, prod(z0, z1))), x2) -> c3(A__ADD(a__prod(mark(x0), a__prod(mark(z0), mark(z1))), mark(x2)), MARK(prod(x0, prod(z0, z1)))) A__ADD(s(prod(x0, p(z0))), x2) -> c3(A__ADD(a__prod(mark(x0), a__p(mark(z0))), mark(x2)), MARK(prod(x0, p(z0)))) A__ADD(s(prod(x0, add(z0, z1))), x2) -> c3(A__ADD(a__prod(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(prod(x0, add(z0, z1)))) A__ADD(s(prod(x0, s(z0))), x2) -> c3(A__ADD(a__prod(mark(x0), s(mark(z0))), mark(x2)), MARK(prod(x0, s(z0)))) A__ADD(s(prod(x0, 0)), x2) -> c3(A__ADD(a__prod(mark(x0), 0), mark(x2)), MARK(prod(x0, 0))) A__ADD(s(prod(x0, true)), x2) -> c3(A__ADD(a__prod(mark(x0), true), mark(x2)), MARK(prod(x0, true))) A__ADD(s(prod(x0, false)), x2) -> c3(A__ADD(a__prod(mark(x0), false), mark(x2)), MARK(prod(x0, false))) A__ADD(s(prod(fact(z0), x1)), x2) -> c3(A__ADD(a__prod(a__fact(mark(z0)), mark(x1)), mark(x2)), MARK(prod(fact(z0), x1))) A__ADD(s(prod(if(z0, z1, z2), x1)), x2) -> c3(A__ADD(a__prod(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(prod(if(z0, z1, z2), x1))) A__ADD(s(prod(zero(z0), x1)), x2) -> c3(A__ADD(a__prod(a__zero(mark(z0)), mark(x1)), mark(x2)), MARK(prod(zero(z0), x1))) A__ADD(s(prod(prod(z0, z1), x1)), x2) -> c3(A__ADD(a__prod(a__prod(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(prod(prod(z0, z1), x1))) A__ADD(s(prod(p(z0), x1)), x2) -> c3(A__ADD(a__prod(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(prod(p(z0), x1))) A__ADD(s(prod(add(z0, z1), x1)), x2) -> c3(A__ADD(a__prod(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(prod(add(z0, z1), x1))) A__ADD(s(prod(s(z0), x1)), x2) -> c3(A__ADD(a__prod(s(mark(z0)), mark(x1)), mark(x2)), MARK(prod(s(z0), x1))) A__ADD(s(prod(0, x1)), x2) -> c3(A__ADD(a__prod(0, mark(x1)), mark(x2)), MARK(prod(0, x1))) A__ADD(s(prod(true, x1)), x2) -> c3(A__ADD(a__prod(true, mark(x1)), mark(x2)), MARK(prod(true, x1))) A__ADD(s(prod(false, x1)), x2) -> c3(A__ADD(a__prod(false, mark(x1)), mark(x2)), MARK(prod(false, x1))) A__ADD(s(prod(x0, x1)), x2) -> c3(MARK(prod(x0, x1))) A__ADD(s(p(fact(z0))), x1) -> c3(A__ADD(a__p(a__fact(mark(z0))), mark(x1)), MARK(p(fact(z0)))) A__ADD(s(p(if(z0, z1, z2))), x1) -> c3(A__ADD(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2)))) A__ADD(s(p(zero(z0))), x1) -> c3(A__ADD(a__p(a__zero(mark(z0))), mark(x1)), MARK(p(zero(z0)))) A__ADD(s(p(prod(z0, z1))), x1) -> c3(A__ADD(a__p(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(p(prod(z0, z1)))) A__ADD(s(p(p(z0))), x1) -> c3(A__ADD(a__p(a__p(mark(z0))), mark(x1)), MARK(p(p(z0)))) A__ADD(s(p(add(z0, z1))), x1) -> c3(A__ADD(a__p(a__add(mark(z0), mark(z1))), mark(x1)), MARK(p(add(z0, z1)))) A__ADD(s(p(s(z0))), x1) -> c3(A__ADD(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0)))) A__ADD(s(p(x0)), x1) -> c3(MARK(p(x0))) A__ADD(s(p(0)), x1) -> c3(A__ADD(a__p(0), mark(x1))) A__ADD(s(p(true)), x1) -> c3(A__ADD(a__p(true), mark(x1))) A__ADD(s(p(false)), x1) -> c3(A__ADD(a__p(false), mark(x1))) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), 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z1))), x1) -> c3(A__ADD(a__fact(a__add(mark(z0), mark(z1))), mark(x1)), MARK(fact(add(z0, z1)))) A__ADD(s(fact(s(z0))), x1) -> c3(A__ADD(a__fact(s(mark(z0))), mark(x1)), MARK(fact(s(z0)))) A__ADD(s(fact(0)), x1) -> c3(A__ADD(a__fact(0), mark(x1)), MARK(fact(0))) A__ADD(s(fact(true)), x1) -> c3(A__ADD(a__fact(true), mark(x1)), MARK(fact(true))) A__ADD(s(fact(false)), x1) -> c3(A__ADD(a__fact(false), mark(x1)), MARK(fact(false))) A__ADD(s(fact(x0)), x1) -> c3(MARK(fact(x0))) A__ADD(s(if(fact(z0), x1, x2)), x3) -> c3(A__ADD(a__if(a__fact(mark(z0)), x1, x2), mark(x3)), MARK(if(fact(z0), x1, x2))) A__ADD(s(if(if(z0, z1, z2), x1, x2)), x3) -> c3(A__ADD(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(if(if(z0, z1, z2), x1, x2))) A__ADD(s(if(zero(z0), x1, x2)), x3) -> c3(A__ADD(a__if(a__zero(mark(z0)), x1, x2), mark(x3)), MARK(if(zero(z0), x1, x2))) A__ADD(s(if(prod(z0, z1), x1, x2)), x3) -> c3(A__ADD(a__if(a__prod(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(prod(z0, z1), x1, x2))) A__ADD(s(if(p(z0), x1, x2)), x3) -> c3(A__ADD(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(if(p(z0), x1, x2))) A__ADD(s(if(add(z0, z1), x1, x2)), x3) -> c3(A__ADD(a__if(a__add(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(add(z0, z1), x1, x2))) A__ADD(s(if(s(z0), x1, x2)), x3) -> c3(A__ADD(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(if(s(z0), x1, x2))) A__ADD(s(if(true, x1, x2)), x3) -> c3(A__ADD(a__if(true, x1, x2), mark(x3)), MARK(if(true, x1, x2))) A__ADD(s(if(false, x1, x2)), x3) -> c3(A__ADD(a__if(false, x1, x2), mark(x3)), MARK(if(false, x1, x2))) A__ADD(s(if(x0, z1, z2)), x3) -> c3(MARK(if(x0, z1, z2))) A__ADD(s(if(0, x1, x2)), x3) -> c3(A__ADD(a__if(0, x1, x2), mark(x3))) A__ADD(s(zero(fact(z0))), x1) -> c3(A__ADD(a__zero(a__fact(mark(z0))), mark(x1)), MARK(zero(fact(z0)))) A__ADD(s(zero(if(z0, z1, z2))), x1) -> c3(A__ADD(a__zero(a__if(mark(z0), z1, z2)), mark(x1)), MARK(zero(if(z0, z1, z2)))) A__ADD(s(zero(zero(z0))), x1) -> c3(A__ADD(a__zero(a__zero(mark(z0))), mark(x1)), MARK(zero(zero(z0)))) A__ADD(s(zero(prod(z0, z1))), x1) -> c3(A__ADD(a__zero(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(zero(prod(z0, z1)))) A__ADD(s(zero(p(z0))), x1) -> c3(A__ADD(a__zero(a__p(mark(z0))), mark(x1)), MARK(zero(p(z0)))) A__ADD(s(zero(add(z0, z1))), x1) -> c3(A__ADD(a__zero(a__add(mark(z0), mark(z1))), mark(x1)), MARK(zero(add(z0, z1)))) A__ADD(s(zero(s(z0))), x1) -> c3(A__ADD(a__zero(s(mark(z0))), mark(x1)), MARK(zero(s(z0)))) A__ADD(s(zero(0)), x1) -> c3(A__ADD(a__zero(0), mark(x1)), MARK(zero(0))) A__ADD(s(zero(true)), x1) -> c3(A__ADD(a__zero(true), mark(x1)), MARK(zero(true))) A__ADD(s(zero(false)), x1) -> c3(A__ADD(a__zero(false), mark(x1)), MARK(zero(false))) A__ADD(s(zero(x0)), x1) -> c3(MARK(zero(x0))) A__ADD(s(prod(x0, fact(z0))), x2) -> c3(A__ADD(a__prod(mark(x0), a__fact(mark(z0))), mark(x2)), MARK(prod(x0, fact(z0)))) A__ADD(s(prod(x0, if(z0, z1, z2))), x2) -> c3(A__ADD(a__prod(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(prod(x0, if(z0, z1, z2)))) A__ADD(s(prod(x0, zero(z0))), x2) -> c3(A__ADD(a__prod(mark(x0), a__zero(mark(z0))), mark(x2)), MARK(prod(x0, zero(z0)))) A__ADD(s(prod(x0, prod(z0, z1))), x2) -> c3(A__ADD(a__prod(mark(x0), a__prod(mark(z0), mark(z1))), mark(x2)), MARK(prod(x0, prod(z0, z1)))) A__ADD(s(prod(x0, p(z0))), x2) -> c3(A__ADD(a__prod(mark(x0), a__p(mark(z0))), mark(x2)), MARK(prod(x0, p(z0)))) A__ADD(s(prod(x0, add(z0, z1))), x2) -> c3(A__ADD(a__prod(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(prod(x0, add(z0, z1)))) A__ADD(s(prod(x0, s(z0))), x2) -> c3(A__ADD(a__prod(mark(x0), s(mark(z0))), mark(x2)), MARK(prod(x0, s(z0)))) A__ADD(s(prod(x0, 0)), x2) -> c3(A__ADD(a__prod(mark(x0), 0), mark(x2)), MARK(prod(x0, 0))) A__ADD(s(prod(x0, true)), x2) -> c3(A__ADD(a__prod(mark(x0), true), mark(x2)), MARK(prod(x0, true))) A__ADD(s(prod(x0, false)), x2) -> c3(A__ADD(a__prod(mark(x0), false), mark(x2)), MARK(prod(x0, false))) A__ADD(s(prod(fact(z0), x1)), x2) -> c3(A__ADD(a__prod(a__fact(mark(z0)), mark(x1)), mark(x2)), MARK(prod(fact(z0), x1))) A__ADD(s(prod(if(z0, z1, z2), x1)), x2) -> c3(A__ADD(a__prod(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(prod(if(z0, z1, z2), x1))) A__ADD(s(prod(zero(z0), x1)), x2) -> c3(A__ADD(a__prod(a__zero(mark(z0)), mark(x1)), mark(x2)), MARK(prod(zero(z0), x1))) A__ADD(s(prod(prod(z0, z1), x1)), x2) -> c3(A__ADD(a__prod(a__prod(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(prod(prod(z0, z1), x1))) A__ADD(s(prod(p(z0), x1)), x2) -> c3(A__ADD(a__prod(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(prod(p(z0), x1))) A__ADD(s(prod(add(z0, z1), x1)), x2) -> c3(A__ADD(a__prod(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(prod(add(z0, z1), x1))) A__ADD(s(prod(s(z0), x1)), x2) -> c3(A__ADD(a__prod(s(mark(z0)), mark(x1)), mark(x2)), MARK(prod(s(z0), x1))) A__ADD(s(prod(0, x1)), x2) -> c3(A__ADD(a__prod(0, mark(x1)), mark(x2)), MARK(prod(0, x1))) A__ADD(s(prod(true, x1)), x2) -> c3(A__ADD(a__prod(true, mark(x1)), mark(x2)), MARK(prod(true, x1))) A__ADD(s(prod(false, x1)), x2) -> c3(A__ADD(a__prod(false, mark(x1)), mark(x2)), MARK(prod(false, x1))) A__ADD(s(prod(x0, x1)), x2) -> c3(MARK(prod(x0, x1))) A__ADD(s(p(fact(z0))), x1) -> c3(A__ADD(a__p(a__fact(mark(z0))), mark(x1)), MARK(p(fact(z0)))) A__ADD(s(p(if(z0, z1, z2))), x1) -> c3(A__ADD(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2)))) A__ADD(s(p(zero(z0))), x1) -> c3(A__ADD(a__p(a__zero(mark(z0))), mark(x1)), MARK(p(zero(z0)))) A__ADD(s(p(prod(z0, z1))), x1) -> c3(A__ADD(a__p(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(p(prod(z0, z1)))) A__ADD(s(p(p(z0))), x1) -> c3(A__ADD(a__p(a__p(mark(z0))), mark(x1)), MARK(p(p(z0)))) A__ADD(s(p(add(z0, z1))), x1) -> c3(A__ADD(a__p(a__add(mark(z0), mark(z1))), mark(x1)), MARK(p(add(z0, z1)))) A__ADD(s(p(s(z0))), x1) -> c3(A__ADD(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0)))) A__ADD(s(p(x0)), x1) -> c3(MARK(p(x0))) A__ADD(s(p(0)), x1) -> c3(A__ADD(a__p(0), mark(x1))) A__ADD(s(p(true)), x1) -> c3(A__ADD(a__p(true), mark(x1))) A__ADD(s(p(false)), x1) -> c3(A__ADD(a__p(false), mark(x1))) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__PROD_2, A__FACT_1 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c27_1, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1, c24_2, c25_2, c25_1, c26_2, c26_1, c_2, c_1 ---------------------------------------- (205) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__ADD(s(add(z0, z1)), x1) -> c3(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) by A__ADD(s(add(x0, x1)), fact(z0)) -> c3(A__ADD(a__add(mark(x0), mark(x1)), a__fact(mark(z0))), MARK(add(x0, x1))) A__ADD(s(add(x0, x1)), if(z0, z1, z2)) -> c3(A__ADD(a__add(mark(x0), mark(x1)), a__if(mark(z0), z1, z2)), MARK(add(x0, x1))) A__ADD(s(add(x0, x1)), zero(z0)) -> c3(A__ADD(a__add(mark(x0), mark(x1)), a__zero(mark(z0))), MARK(add(x0, x1))) A__ADD(s(add(x0, x1)), prod(z0, z1)) -> c3(A__ADD(a__add(mark(x0), mark(x1)), a__prod(mark(z0), mark(z1))), MARK(add(x0, x1))) A__ADD(s(add(x0, x1)), p(z0)) -> c3(A__ADD(a__add(mark(x0), mark(x1)), a__p(mark(z0))), MARK(add(x0, x1))) A__ADD(s(add(x0, x1)), add(z0, z1)) -> c3(A__ADD(a__add(mark(x0), mark(x1)), a__add(mark(z0), mark(z1))), MARK(add(x0, x1))) A__ADD(s(add(x0, x1)), s(z0)) -> c3(A__ADD(a__add(mark(x0), mark(x1)), s(mark(z0))), MARK(add(x0, x1))) A__ADD(s(add(x0, x1)), 0) -> c3(A__ADD(a__add(mark(x0), mark(x1)), 0), MARK(add(x0, x1))) A__ADD(s(add(x0, x1)), true) -> c3(A__ADD(a__add(mark(x0), mark(x1)), true), MARK(add(x0, x1))) A__ADD(s(add(x0, x1)), false) -> c3(A__ADD(a__add(mark(x0), mark(x1)), false), MARK(add(x0, x1))) A__ADD(s(add(x0, x1)), x2) -> c3(A__ADD(add(mark(x0), mark(x1)), mark(x2)), MARK(add(x0, x1))) A__ADD(s(add(x0, fact(z0))), x2) -> c3(A__ADD(a__add(mark(x0), a__fact(mark(z0))), mark(x2)), MARK(add(x0, fact(z0)))) A__ADD(s(add(x0, if(z0, z1, z2))), x2) -> c3(A__ADD(a__add(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(add(x0, if(z0, z1, z2)))) A__ADD(s(add(x0, zero(z0))), x2) -> c3(A__ADD(a__add(mark(x0), a__zero(mark(z0))), mark(x2)), MARK(add(x0, zero(z0)))) A__ADD(s(add(x0, prod(z0, z1))), x2) -> c3(A__ADD(a__add(mark(x0), a__prod(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, prod(z0, z1)))) A__ADD(s(add(x0, p(z0))), x2) -> c3(A__ADD(a__add(mark(x0), a__p(mark(z0))), mark(x2)), MARK(add(x0, p(z0)))) A__ADD(s(add(x0, add(z0, z1))), x2) -> c3(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, add(z0, z1)))) A__ADD(s(add(x0, s(z0))), x2) -> c3(A__ADD(a__add(mark(x0), s(mark(z0))), mark(x2)), MARK(add(x0, s(z0)))) A__ADD(s(add(x0, 0)), x2) -> c3(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(add(x0, 0))) A__ADD(s(add(x0, true)), x2) -> c3(A__ADD(a__add(mark(x0), true), mark(x2)), MARK(add(x0, true))) A__ADD(s(add(x0, false)), x2) -> c3(A__ADD(a__add(mark(x0), false), mark(x2)), MARK(add(x0, false))) A__ADD(s(add(fact(z0), x1)), x2) -> c3(A__ADD(a__add(a__fact(mark(z0)), mark(x1)), mark(x2)), MARK(add(fact(z0), x1))) A__ADD(s(add(if(z0, z1, z2), x1)), x2) -> c3(A__ADD(a__add(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(add(if(z0, z1, z2), x1))) A__ADD(s(add(zero(z0), x1)), x2) -> c3(A__ADD(a__add(a__zero(mark(z0)), mark(x1)), mark(x2)), MARK(add(zero(z0), x1))) A__ADD(s(add(prod(z0, z1), x1)), x2) -> c3(A__ADD(a__add(a__prod(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(prod(z0, z1), x1))) A__ADD(s(add(p(z0), x1)), x2) -> c3(A__ADD(a__add(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(add(p(z0), x1))) A__ADD(s(add(add(z0, z1), x1)), x2) -> c3(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(add(z0, z1), x1))) A__ADD(s(add(s(z0), x1)), x2) -> c3(A__ADD(a__add(s(mark(z0)), mark(x1)), mark(x2)), MARK(add(s(z0), x1))) A__ADD(s(add(0, x1)), x2) -> c3(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(add(0, x1))) A__ADD(s(add(true, x1)), x2) -> c3(A__ADD(a__add(true, mark(x1)), mark(x2)), MARK(add(true, x1))) A__ADD(s(add(false, x1)), x2) -> c3(A__ADD(a__add(false, mark(x1)), mark(x2)), MARK(add(false, x1))) ---------------------------------------- (206) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> 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A__ADD(s(prod(p(z0), x1)), x2) -> c3(A__ADD(a__prod(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(prod(p(z0), x1))) A__ADD(s(prod(add(z0, z1), x1)), x2) -> c3(A__ADD(a__prod(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(prod(add(z0, z1), x1))) A__ADD(s(prod(s(z0), x1)), x2) -> c3(A__ADD(a__prod(s(mark(z0)), mark(x1)), mark(x2)), MARK(prod(s(z0), x1))) A__ADD(s(prod(0, x1)), x2) -> c3(A__ADD(a__prod(0, mark(x1)), mark(x2)), MARK(prod(0, x1))) A__ADD(s(prod(true, x1)), x2) -> c3(A__ADD(a__prod(true, mark(x1)), mark(x2)), MARK(prod(true, x1))) A__ADD(s(prod(false, x1)), x2) -> c3(A__ADD(a__prod(false, mark(x1)), mark(x2)), MARK(prod(false, x1))) A__ADD(s(prod(x0, x1)), x2) -> c3(MARK(prod(x0, x1))) A__ADD(s(p(fact(z0))), x1) -> c3(A__ADD(a__p(a__fact(mark(z0))), mark(x1)), MARK(p(fact(z0)))) A__ADD(s(p(if(z0, z1, z2))), x1) -> c3(A__ADD(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2)))) A__ADD(s(p(zero(z0))), x1) -> c3(A__ADD(a__p(a__zero(mark(z0))), mark(x1)), 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A__ADD(s(add(if(z0, z1, z2), x1)), x2) -> c3(A__ADD(a__add(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(add(if(z0, z1, z2), x1))) A__ADD(s(add(zero(z0), x1)), x2) -> c3(A__ADD(a__add(a__zero(mark(z0)), mark(x1)), mark(x2)), MARK(add(zero(z0), x1))) A__ADD(s(add(prod(z0, z1), x1)), x2) -> c3(A__ADD(a__add(a__prod(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(prod(z0, z1), x1))) A__ADD(s(add(p(z0), x1)), x2) -> c3(A__ADD(a__add(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(add(p(z0), x1))) A__ADD(s(add(add(z0, z1), x1)), x2) -> c3(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(add(z0, z1), x1))) A__ADD(s(add(s(z0), x1)), x2) -> c3(A__ADD(a__add(s(mark(z0)), mark(x1)), mark(x2)), MARK(add(s(z0), x1))) A__ADD(s(add(0, x1)), x2) -> c3(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(add(0, x1))) A__ADD(s(add(true, x1)), x2) -> c3(A__ADD(a__add(true, mark(x1)), mark(x2)), MARK(add(true, x1))) A__ADD(s(add(false, x1)), x2) -> c3(A__ADD(a__add(false, mark(x1)), mark(x2)), MARK(add(false, x1))) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1)))) A__ADD(s(x0), prod(x1, x2)) -> c3(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), prod(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, p(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, s(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, 0)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), prod(x1, true)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(x0)) A__ADD(s(x0), prod(x1, false)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(x0)) A__ADD(s(x0), prod(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(p(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(0, x2)) -> c3(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(true, x2)) -> c3(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(false, x2)) -> c3(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), prod(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2)))) A__ADD(s(x0), p(x1)) -> c3(A__ADD(mark(x0), p(mark(x1))), MARK(x0)) A__ADD(s(x0), p(fact(z0))) -> c3(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), p(zero(z0))) -> c3(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(p(z0))) -> c3(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(add(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(s(z0))) -> c3(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(0)) -> c3(A__ADD(mark(x0), a__p(0)), MARK(x0)) A__ADD(s(x0), p(true)) -> c3(A__ADD(mark(x0), a__p(true)), MARK(x0)) A__ADD(s(x0), p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> 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c3(A__ADD(a__p(a__p(mark(z0))), mark(x1)), MARK(p(p(z0)))) A__ADD(s(p(add(z0, z1))), x1) -> c3(A__ADD(a__p(a__add(mark(z0), mark(z1))), mark(x1)), MARK(p(add(z0, z1)))) A__ADD(s(p(s(z0))), x1) -> c3(A__ADD(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0)))) A__ADD(s(p(x0)), x1) -> c3(MARK(p(x0))) A__ADD(s(p(0)), x1) -> c3(A__ADD(a__p(0), mark(x1))) A__ADD(s(p(true)), x1) -> c3(A__ADD(a__p(true), mark(x1))) A__ADD(s(p(false)), x1) -> c3(A__ADD(a__p(false), mark(x1))) A__ADD(s(add(x0, x1)), x2) -> c3(A__ADD(add(mark(x0), mark(x1)), mark(x2)), MARK(add(x0, x1))) A__ADD(s(add(x0, fact(z0))), x2) -> c3(A__ADD(a__add(mark(x0), a__fact(mark(z0))), mark(x2)), MARK(add(x0, fact(z0)))) A__ADD(s(add(x0, if(z0, z1, z2))), x2) -> c3(A__ADD(a__add(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(add(x0, if(z0, z1, z2)))) A__ADD(s(add(x0, zero(z0))), x2) -> c3(A__ADD(a__add(mark(x0), a__zero(mark(z0))), mark(x2)), MARK(add(x0, zero(z0)))) A__ADD(s(add(x0, prod(z0, z1))), x2) -> c3(A__ADD(a__add(mark(x0), a__prod(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, prod(z0, z1)))) A__ADD(s(add(x0, p(z0))), x2) -> c3(A__ADD(a__add(mark(x0), a__p(mark(z0))), mark(x2)), MARK(add(x0, p(z0)))) A__ADD(s(add(x0, add(z0, z1))), x2) -> c3(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, add(z0, z1)))) A__ADD(s(add(x0, s(z0))), x2) -> c3(A__ADD(a__add(mark(x0), s(mark(z0))), mark(x2)), MARK(add(x0, s(z0)))) A__ADD(s(add(x0, 0)), x2) -> c3(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(add(x0, 0))) A__ADD(s(add(x0, true)), x2) -> c3(A__ADD(a__add(mark(x0), true), mark(x2)), MARK(add(x0, true))) A__ADD(s(add(x0, false)), x2) -> c3(A__ADD(a__add(mark(x0), false), mark(x2)), MARK(add(x0, false))) A__ADD(s(add(fact(z0), x1)), x2) -> c3(A__ADD(a__add(a__fact(mark(z0)), mark(x1)), mark(x2)), MARK(add(fact(z0), x1))) A__ADD(s(add(if(z0, z1, z2), x1)), x2) -> c3(A__ADD(a__add(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(add(if(z0, z1, z2), x1))) A__ADD(s(add(zero(z0), x1)), x2) -> c3(A__ADD(a__add(a__zero(mark(z0)), mark(x1)), mark(x2)), MARK(add(zero(z0), x1))) A__ADD(s(add(prod(z0, z1), x1)), x2) -> c3(A__ADD(a__add(a__prod(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(prod(z0, z1), x1))) A__ADD(s(add(p(z0), x1)), x2) -> c3(A__ADD(a__add(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(add(p(z0), x1))) A__ADD(s(add(add(z0, z1), x1)), x2) -> c3(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(add(z0, z1), x1))) A__ADD(s(add(s(z0), x1)), x2) -> c3(A__ADD(a__add(s(mark(z0)), mark(x1)), mark(x2)), MARK(add(s(z0), x1))) A__ADD(s(add(0, x1)), x2) -> c3(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(add(0, x1))) A__ADD(s(add(true, x1)), x2) -> c3(A__ADD(a__add(true, mark(x1)), mark(x2)), MARK(add(true, x1))) A__ADD(s(add(false, x1)), x2) -> c3(A__ADD(a__add(false, mark(x1)), mark(x2)), MARK(add(false, x1))) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__PROD_2, A__FACT_1 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c27_1, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1, c24_2, c25_2, c25_1, c26_2, c26_1, c_2, c_1 ---------------------------------------- (207) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (208) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1)))) A__ADD(s(x0), prod(x1, x2)) -> c3(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), prod(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, p(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, s(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, 0)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), prod(x1, true)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(x0)) A__ADD(s(x0), prod(x1, false)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(x0)) A__ADD(s(x0), prod(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(p(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(0, x2)) -> c3(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(true, x2)) -> c3(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(false, x2)) -> c3(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), prod(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2)))) A__ADD(s(x0), p(x1)) -> c3(A__ADD(mark(x0), p(mark(x1))), MARK(x0)) A__ADD(s(x0), p(fact(z0))) -> c3(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), p(zero(z0))) -> c3(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(p(z0))) -> c3(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(add(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(s(z0))) -> c3(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(0)) -> c3(A__ADD(mark(x0), a__p(0)), MARK(x0)) A__ADD(s(x0), p(true)) -> c3(A__ADD(mark(x0), a__p(true)), MARK(x0)) A__ADD(s(x0), p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1)))) A__ADD(s(x0), add(x1, x2)) -> c3(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), add(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), add(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, p(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, s(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, 0)) -> c3(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), add(x1, true)) -> c3(A__ADD(mark(x0), a__add(mark(x1), true)), MARK(x0)) A__ADD(s(x0), add(x1, false)) -> c3(A__ADD(mark(x0), a__add(mark(x1), false)), MARK(x0)) A__ADD(s(x0), add(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), add(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(p(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(s(z0), x2)) -> c3(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(0, x2)) -> c3(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) A__ADD(s(x0), add(true, x2)) -> c3(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(x0)) A__ADD(s(x0), add(false, x2)) -> c3(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), add(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), add(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), add(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__add(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), add(x1, x2)) -> c3(A__ADD(0, a__add(mark(x1), mark(x2)))) A__ADD(s(x0), s(fact(z0))) -> c3(A__ADD(mark(x0), s(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), s(zero(z0))) -> c3(A__ADD(mark(x0), s(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(prod(z0, z1))) -> c3(A__ADD(mark(x0), s(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(p(z0))) -> c3(A__ADD(mark(x0), s(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(add(z0, z1))) -> c3(A__ADD(mark(x0), s(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(s(z0))) -> c3(A__ADD(mark(x0), s(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(0)) -> c3(A__ADD(mark(x0), s(0)), MARK(x0)) A__ADD(s(x0), s(true)) -> c3(A__ADD(mark(x0), s(true)), MARK(x0)) A__ADD(s(x0), s(false)) -> c3(A__ADD(mark(x0), s(false)), MARK(x0)) A__ADD(s(fact(z0)), s(x1)) -> c3(A__ADD(a__fact(mark(z0)), s(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), s(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), s(x1)) -> c3(A__ADD(a__zero(mark(z0)), s(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), s(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), s(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), s(x1)) -> c3(A__ADD(a__p(mark(z0)), s(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), s(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), s(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), s(x1)) -> c3(A__ADD(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__ADD(s(0), s(x1)) -> c3(A__ADD(0, s(mark(x1)))) A__ADD(s(fact(z0)), 0) -> c3(A__ADD(a__fact(mark(z0)), 0), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), 0) -> c3(A__ADD(a__if(mark(z0), z1, z2), 0), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), 0) -> c3(A__ADD(a__zero(mark(z0)), 0), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), 0) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), 0), MARK(prod(z0, z1))) A__ADD(s(p(z0)), 0) -> c3(A__ADD(a__p(mark(z0)), 0), MARK(p(z0))) A__ADD(s(add(z0, z1)), 0) -> c3(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) A__ADD(s(s(z0)), 0) -> c3(A__ADD(s(mark(z0)), 0), MARK(s(z0))) A__ADD(s(0), 0) -> c3(A__ADD(0, 0)) A__ADD(s(fact(z0)), true) -> c3(A__ADD(a__fact(mark(z0)), true), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), true) -> c3(A__ADD(a__if(mark(z0), z1, z2), true), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), true) -> c3(A__ADD(a__zero(mark(z0)), true), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), true) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), true), MARK(prod(z0, z1))) A__ADD(s(p(z0)), true) -> c3(A__ADD(a__p(mark(z0)), true), MARK(p(z0))) A__ADD(s(add(z0, z1)), true) -> c3(A__ADD(a__add(mark(z0), mark(z1)), true), MARK(add(z0, z1))) A__ADD(s(s(z0)), true) -> c3(A__ADD(s(mark(z0)), true), MARK(s(z0))) A__ADD(s(0), true) -> c3(A__ADD(0, true)) A__ADD(s(fact(z0)), false) -> c3(A__ADD(a__fact(mark(z0)), false), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), false) -> c3(A__ADD(a__if(mark(z0), z1, z2), false), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), false) -> c3(A__ADD(a__zero(mark(z0)), false), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), false) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), false), MARK(prod(z0, z1))) A__ADD(s(p(z0)), false) -> c3(A__ADD(a__p(mark(z0)), false), MARK(p(z0))) A__ADD(s(add(z0, z1)), false) -> c3(A__ADD(a__add(mark(z0), mark(z1)), false), MARK(add(z0, z1))) A__ADD(s(s(z0)), false) -> c3(A__ADD(s(mark(z0)), false), MARK(s(z0))) A__ADD(s(0), false) -> c3(A__ADD(0, false)) A__ADD(s(fact(x0)), x1) -> c3(A__ADD(a__if(a__zero(mark(mark(x0))), s(0), prod(mark(x0), fact(p(mark(x0))))), mark(x1)), MARK(fact(x0))) A__ADD(s(fact(fact(z0))), x1) -> c3(A__ADD(a__fact(a__fact(mark(z0))), mark(x1)), MARK(fact(fact(z0)))) A__ADD(s(fact(if(z0, z1, z2))), x1) -> c3(A__ADD(a__fact(a__if(mark(z0), z1, z2)), mark(x1)), MARK(fact(if(z0, z1, z2)))) A__ADD(s(fact(zero(z0))), x1) -> c3(A__ADD(a__fact(a__zero(mark(z0))), mark(x1)), MARK(fact(zero(z0)))) A__ADD(s(fact(prod(z0, z1))), x1) -> c3(A__ADD(a__fact(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(fact(prod(z0, z1)))) A__ADD(s(fact(p(z0))), x1) -> c3(A__ADD(a__fact(a__p(mark(z0))), mark(x1)), MARK(fact(p(z0)))) A__ADD(s(fact(add(z0, z1))), x1) -> c3(A__ADD(a__fact(a__add(mark(z0), mark(z1))), mark(x1)), MARK(fact(add(z0, z1)))) A__ADD(s(fact(s(z0))), x1) -> c3(A__ADD(a__fact(s(mark(z0))), mark(x1)), MARK(fact(s(z0)))) A__ADD(s(fact(0)), x1) -> c3(A__ADD(a__fact(0), mark(x1)), MARK(fact(0))) A__ADD(s(fact(true)), x1) -> c3(A__ADD(a__fact(true), mark(x1)), MARK(fact(true))) A__ADD(s(fact(false)), x1) -> c3(A__ADD(a__fact(false), mark(x1)), MARK(fact(false))) A__ADD(s(fact(x0)), x1) -> c3(MARK(fact(x0))) A__ADD(s(if(fact(z0), x1, x2)), x3) -> c3(A__ADD(a__if(a__fact(mark(z0)), x1, x2), mark(x3)), MARK(if(fact(z0), x1, x2))) A__ADD(s(if(if(z0, z1, z2), x1, x2)), x3) -> c3(A__ADD(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(if(if(z0, z1, z2), x1, x2))) A__ADD(s(if(zero(z0), x1, x2)), x3) -> c3(A__ADD(a__if(a__zero(mark(z0)), x1, x2), mark(x3)), MARK(if(zero(z0), x1, x2))) A__ADD(s(if(prod(z0, z1), x1, x2)), x3) -> c3(A__ADD(a__if(a__prod(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(prod(z0, z1), x1, x2))) A__ADD(s(if(p(z0), x1, x2)), x3) -> c3(A__ADD(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(if(p(z0), x1, x2))) A__ADD(s(if(add(z0, z1), x1, x2)), x3) -> c3(A__ADD(a__if(a__add(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(add(z0, z1), x1, x2))) A__ADD(s(if(s(z0), x1, x2)), x3) -> c3(A__ADD(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(if(s(z0), x1, x2))) A__ADD(s(if(true, x1, x2)), x3) -> c3(A__ADD(a__if(true, x1, x2), mark(x3)), MARK(if(true, x1, x2))) A__ADD(s(if(false, x1, x2)), x3) -> c3(A__ADD(a__if(false, x1, x2), mark(x3)), MARK(if(false, x1, x2))) A__ADD(s(if(x0, z1, z2)), x3) -> c3(MARK(if(x0, z1, z2))) A__ADD(s(if(0, x1, x2)), x3) -> c3(A__ADD(a__if(0, x1, x2), mark(x3))) A__ADD(s(zero(fact(z0))), x1) -> c3(A__ADD(a__zero(a__fact(mark(z0))), mark(x1)), MARK(zero(fact(z0)))) A__ADD(s(zero(if(z0, z1, z2))), x1) -> c3(A__ADD(a__zero(a__if(mark(z0), z1, z2)), mark(x1)), MARK(zero(if(z0, z1, z2)))) A__ADD(s(zero(zero(z0))), x1) -> c3(A__ADD(a__zero(a__zero(mark(z0))), mark(x1)), MARK(zero(zero(z0)))) A__ADD(s(zero(prod(z0, z1))), x1) -> c3(A__ADD(a__zero(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(zero(prod(z0, z1)))) A__ADD(s(zero(p(z0))), x1) -> c3(A__ADD(a__zero(a__p(mark(z0))), mark(x1)), MARK(zero(p(z0)))) A__ADD(s(zero(add(z0, z1))), x1) -> c3(A__ADD(a__zero(a__add(mark(z0), mark(z1))), mark(x1)), MARK(zero(add(z0, z1)))) A__ADD(s(zero(s(z0))), x1) -> c3(A__ADD(a__zero(s(mark(z0))), mark(x1)), MARK(zero(s(z0)))) A__ADD(s(zero(0)), x1) -> c3(A__ADD(a__zero(0), mark(x1)), MARK(zero(0))) A__ADD(s(zero(true)), x1) -> c3(A__ADD(a__zero(true), mark(x1)), MARK(zero(true))) A__ADD(s(zero(false)), x1) -> c3(A__ADD(a__zero(false), mark(x1)), MARK(zero(false))) A__ADD(s(zero(x0)), x1) -> c3(MARK(zero(x0))) A__ADD(s(prod(x0, fact(z0))), x2) -> c3(A__ADD(a__prod(mark(x0), a__fact(mark(z0))), mark(x2)), MARK(prod(x0, fact(z0)))) A__ADD(s(prod(x0, if(z0, z1, z2))), x2) -> c3(A__ADD(a__prod(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(prod(x0, if(z0, z1, z2)))) A__ADD(s(prod(x0, zero(z0))), x2) -> c3(A__ADD(a__prod(mark(x0), a__zero(mark(z0))), mark(x2)), MARK(prod(x0, zero(z0)))) A__ADD(s(prod(x0, prod(z0, z1))), x2) -> c3(A__ADD(a__prod(mark(x0), a__prod(mark(z0), mark(z1))), mark(x2)), MARK(prod(x0, prod(z0, z1)))) A__ADD(s(prod(x0, p(z0))), x2) -> c3(A__ADD(a__prod(mark(x0), a__p(mark(z0))), mark(x2)), MARK(prod(x0, p(z0)))) A__ADD(s(prod(x0, add(z0, z1))), x2) -> c3(A__ADD(a__prod(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(prod(x0, add(z0, z1)))) A__ADD(s(prod(x0, s(z0))), x2) -> c3(A__ADD(a__prod(mark(x0), s(mark(z0))), mark(x2)), MARK(prod(x0, s(z0)))) A__ADD(s(prod(x0, 0)), x2) -> c3(A__ADD(a__prod(mark(x0), 0), mark(x2)), MARK(prod(x0, 0))) A__ADD(s(prod(x0, true)), x2) -> c3(A__ADD(a__prod(mark(x0), true), mark(x2)), MARK(prod(x0, true))) A__ADD(s(prod(x0, false)), x2) -> c3(A__ADD(a__prod(mark(x0), false), mark(x2)), MARK(prod(x0, false))) A__ADD(s(prod(fact(z0), x1)), x2) -> c3(A__ADD(a__prod(a__fact(mark(z0)), mark(x1)), mark(x2)), MARK(prod(fact(z0), x1))) A__ADD(s(prod(if(z0, z1, z2), x1)), x2) -> c3(A__ADD(a__prod(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(prod(if(z0, z1, z2), x1))) A__ADD(s(prod(zero(z0), x1)), x2) -> c3(A__ADD(a__prod(a__zero(mark(z0)), mark(x1)), mark(x2)), MARK(prod(zero(z0), x1))) A__ADD(s(prod(prod(z0, z1), x1)), x2) -> c3(A__ADD(a__prod(a__prod(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(prod(prod(z0, z1), x1))) A__ADD(s(prod(p(z0), x1)), x2) -> c3(A__ADD(a__prod(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(prod(p(z0), x1))) A__ADD(s(prod(add(z0, z1), x1)), x2) -> c3(A__ADD(a__prod(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(prod(add(z0, z1), x1))) A__ADD(s(prod(s(z0), x1)), x2) -> c3(A__ADD(a__prod(s(mark(z0)), mark(x1)), mark(x2)), MARK(prod(s(z0), x1))) A__ADD(s(prod(0, x1)), x2) -> c3(A__ADD(a__prod(0, mark(x1)), mark(x2)), MARK(prod(0, x1))) A__ADD(s(prod(true, x1)), x2) -> c3(A__ADD(a__prod(true, mark(x1)), mark(x2)), MARK(prod(true, x1))) A__ADD(s(prod(false, x1)), x2) -> c3(A__ADD(a__prod(false, mark(x1)), mark(x2)), MARK(prod(false, x1))) A__ADD(s(prod(x0, x1)), x2) -> c3(MARK(prod(x0, x1))) A__ADD(s(p(fact(z0))), x1) -> c3(A__ADD(a__p(a__fact(mark(z0))), mark(x1)), MARK(p(fact(z0)))) A__ADD(s(p(if(z0, z1, z2))), x1) -> c3(A__ADD(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2)))) A__ADD(s(p(zero(z0))), x1) -> c3(A__ADD(a__p(a__zero(mark(z0))), mark(x1)), MARK(p(zero(z0)))) A__ADD(s(p(prod(z0, z1))), x1) -> c3(A__ADD(a__p(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(p(prod(z0, z1)))) A__ADD(s(p(p(z0))), x1) -> c3(A__ADD(a__p(a__p(mark(z0))), mark(x1)), MARK(p(p(z0)))) A__ADD(s(p(add(z0, z1))), x1) -> c3(A__ADD(a__p(a__add(mark(z0), mark(z1))), mark(x1)), MARK(p(add(z0, z1)))) A__ADD(s(p(s(z0))), x1) -> c3(A__ADD(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0)))) A__ADD(s(p(x0)), x1) -> c3(MARK(p(x0))) A__ADD(s(p(0)), x1) -> c3(A__ADD(a__p(0), mark(x1))) A__ADD(s(p(true)), x1) -> c3(A__ADD(a__p(true), mark(x1))) A__ADD(s(p(false)), x1) -> c3(A__ADD(a__p(false), mark(x1))) A__ADD(s(add(x0, fact(z0))), x2) -> c3(A__ADD(a__add(mark(x0), a__fact(mark(z0))), mark(x2)), MARK(add(x0, fact(z0)))) A__ADD(s(add(x0, if(z0, z1, z2))), x2) -> c3(A__ADD(a__add(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(add(x0, if(z0, z1, z2)))) A__ADD(s(add(x0, zero(z0))), x2) -> c3(A__ADD(a__add(mark(x0), a__zero(mark(z0))), mark(x2)), MARK(add(x0, zero(z0)))) A__ADD(s(add(x0, prod(z0, z1))), x2) -> c3(A__ADD(a__add(mark(x0), a__prod(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, prod(z0, z1)))) A__ADD(s(add(x0, p(z0))), x2) -> c3(A__ADD(a__add(mark(x0), a__p(mark(z0))), mark(x2)), MARK(add(x0, p(z0)))) A__ADD(s(add(x0, add(z0, z1))), x2) -> c3(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, add(z0, z1)))) A__ADD(s(add(x0, s(z0))), x2) -> c3(A__ADD(a__add(mark(x0), s(mark(z0))), mark(x2)), MARK(add(x0, s(z0)))) A__ADD(s(add(x0, 0)), x2) -> c3(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(add(x0, 0))) A__ADD(s(add(x0, true)), x2) -> c3(A__ADD(a__add(mark(x0), true), mark(x2)), MARK(add(x0, true))) A__ADD(s(add(x0, false)), x2) -> c3(A__ADD(a__add(mark(x0), false), mark(x2)), MARK(add(x0, false))) A__ADD(s(add(fact(z0), x1)), x2) -> c3(A__ADD(a__add(a__fact(mark(z0)), mark(x1)), mark(x2)), MARK(add(fact(z0), x1))) A__ADD(s(add(if(z0, z1, z2), x1)), x2) -> c3(A__ADD(a__add(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(add(if(z0, z1, z2), x1))) A__ADD(s(add(zero(z0), x1)), x2) -> c3(A__ADD(a__add(a__zero(mark(z0)), mark(x1)), mark(x2)), MARK(add(zero(z0), x1))) A__ADD(s(add(prod(z0, z1), x1)), x2) -> c3(A__ADD(a__add(a__prod(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(prod(z0, z1), x1))) A__ADD(s(add(p(z0), x1)), x2) -> c3(A__ADD(a__add(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(add(p(z0), x1))) A__ADD(s(add(add(z0, z1), x1)), x2) -> c3(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(add(z0, z1), x1))) A__ADD(s(add(s(z0), x1)), x2) -> c3(A__ADD(a__add(s(mark(z0)), mark(x1)), mark(x2)), MARK(add(s(z0), x1))) A__ADD(s(add(0, x1)), x2) -> c3(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(add(0, x1))) A__ADD(s(add(true, x1)), x2) -> c3(A__ADD(a__add(true, mark(x1)), mark(x2)), MARK(add(true, x1))) A__ADD(s(add(false, x1)), x2) -> c3(A__ADD(a__add(false, mark(x1)), mark(x2)), MARK(add(false, x1))) A__ADD(s(add(x0, x1)), x2) -> c3(MARK(add(x0, x1))) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1)))) A__ADD(s(x0), prod(x1, x2)) -> c3(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) 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mark(x1)), MARK(fact(fact(z0)))) A__ADD(s(fact(if(z0, z1, z2))), x1) -> c3(A__ADD(a__fact(a__if(mark(z0), z1, z2)), mark(x1)), MARK(fact(if(z0, z1, z2)))) A__ADD(s(fact(zero(z0))), x1) -> c3(A__ADD(a__fact(a__zero(mark(z0))), mark(x1)), MARK(fact(zero(z0)))) A__ADD(s(fact(prod(z0, z1))), x1) -> c3(A__ADD(a__fact(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(fact(prod(z0, z1)))) A__ADD(s(fact(p(z0))), x1) -> c3(A__ADD(a__fact(a__p(mark(z0))), mark(x1)), MARK(fact(p(z0)))) A__ADD(s(fact(add(z0, z1))), x1) -> c3(A__ADD(a__fact(a__add(mark(z0), mark(z1))), mark(x1)), MARK(fact(add(z0, z1)))) A__ADD(s(fact(s(z0))), x1) -> c3(A__ADD(a__fact(s(mark(z0))), mark(x1)), MARK(fact(s(z0)))) A__ADD(s(fact(0)), x1) -> c3(A__ADD(a__fact(0), mark(x1)), MARK(fact(0))) A__ADD(s(fact(true)), x1) -> c3(A__ADD(a__fact(true), mark(x1)), MARK(fact(true))) A__ADD(s(fact(false)), x1) -> c3(A__ADD(a__fact(false), mark(x1)), MARK(fact(false))) A__ADD(s(fact(x0)), x1) -> c3(MARK(fact(x0))) A__ADD(s(if(fact(z0), x1, x2)), x3) -> c3(A__ADD(a__if(a__fact(mark(z0)), x1, x2), mark(x3)), MARK(if(fact(z0), x1, x2))) A__ADD(s(if(if(z0, z1, z2), x1, x2)), x3) -> c3(A__ADD(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(if(if(z0, z1, z2), x1, x2))) A__ADD(s(if(zero(z0), x1, x2)), x3) -> c3(A__ADD(a__if(a__zero(mark(z0)), x1, x2), mark(x3)), MARK(if(zero(z0), x1, x2))) A__ADD(s(if(prod(z0, z1), x1, x2)), x3) -> c3(A__ADD(a__if(a__prod(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(prod(z0, z1), x1, x2))) A__ADD(s(if(p(z0), x1, x2)), x3) -> c3(A__ADD(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(if(p(z0), x1, x2))) A__ADD(s(if(add(z0, z1), x1, x2)), x3) -> c3(A__ADD(a__if(a__add(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(add(z0, z1), x1, x2))) A__ADD(s(if(s(z0), x1, x2)), x3) -> c3(A__ADD(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(if(s(z0), x1, x2))) A__ADD(s(if(true, x1, x2)), x3) -> c3(A__ADD(a__if(true, x1, x2), mark(x3)), MARK(if(true, x1, x2))) A__ADD(s(if(false, x1, x2)), x3) -> c3(A__ADD(a__if(false, x1, x2), mark(x3)), MARK(if(false, x1, x2))) A__ADD(s(if(x0, z1, z2)), x3) -> c3(MARK(if(x0, z1, z2))) A__ADD(s(if(0, x1, x2)), x3) -> c3(A__ADD(a__if(0, x1, x2), mark(x3))) A__ADD(s(zero(fact(z0))), x1) -> c3(A__ADD(a__zero(a__fact(mark(z0))), mark(x1)), MARK(zero(fact(z0)))) A__ADD(s(zero(if(z0, z1, z2))), x1) -> c3(A__ADD(a__zero(a__if(mark(z0), z1, z2)), mark(x1)), MARK(zero(if(z0, z1, z2)))) A__ADD(s(zero(zero(z0))), x1) -> c3(A__ADD(a__zero(a__zero(mark(z0))), mark(x1)), MARK(zero(zero(z0)))) A__ADD(s(zero(prod(z0, z1))), x1) -> c3(A__ADD(a__zero(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(zero(prod(z0, z1)))) A__ADD(s(zero(p(z0))), x1) -> c3(A__ADD(a__zero(a__p(mark(z0))), mark(x1)), MARK(zero(p(z0)))) A__ADD(s(zero(add(z0, z1))), x1) -> c3(A__ADD(a__zero(a__add(mark(z0), mark(z1))), mark(x1)), MARK(zero(add(z0, z1)))) A__ADD(s(zero(s(z0))), x1) -> c3(A__ADD(a__zero(s(mark(z0))), mark(x1)), MARK(zero(s(z0)))) A__ADD(s(zero(0)), x1) -> c3(A__ADD(a__zero(0), mark(x1)), MARK(zero(0))) A__ADD(s(zero(true)), x1) -> c3(A__ADD(a__zero(true), mark(x1)), MARK(zero(true))) A__ADD(s(zero(false)), x1) -> c3(A__ADD(a__zero(false), mark(x1)), MARK(zero(false))) A__ADD(s(zero(x0)), x1) -> c3(MARK(zero(x0))) A__ADD(s(prod(x0, fact(z0))), x2) -> c3(A__ADD(a__prod(mark(x0), a__fact(mark(z0))), mark(x2)), MARK(prod(x0, fact(z0)))) A__ADD(s(prod(x0, if(z0, z1, z2))), x2) -> c3(A__ADD(a__prod(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(prod(x0, if(z0, z1, z2)))) A__ADD(s(prod(x0, zero(z0))), x2) -> c3(A__ADD(a__prod(mark(x0), a__zero(mark(z0))), mark(x2)), MARK(prod(x0, zero(z0)))) A__ADD(s(prod(x0, prod(z0, z1))), x2) -> c3(A__ADD(a__prod(mark(x0), a__prod(mark(z0), mark(z1))), mark(x2)), MARK(prod(x0, prod(z0, z1)))) A__ADD(s(prod(x0, p(z0))), x2) -> c3(A__ADD(a__prod(mark(x0), a__p(mark(z0))), mark(x2)), MARK(prod(x0, p(z0)))) A__ADD(s(prod(x0, add(z0, z1))), x2) -> c3(A__ADD(a__prod(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(prod(x0, add(z0, z1)))) A__ADD(s(prod(x0, s(z0))), x2) -> c3(A__ADD(a__prod(mark(x0), s(mark(z0))), mark(x2)), MARK(prod(x0, s(z0)))) A__ADD(s(prod(x0, 0)), x2) -> c3(A__ADD(a__prod(mark(x0), 0), mark(x2)), MARK(prod(x0, 0))) A__ADD(s(prod(x0, true)), x2) -> c3(A__ADD(a__prod(mark(x0), true), mark(x2)), MARK(prod(x0, true))) A__ADD(s(prod(x0, false)), x2) -> c3(A__ADD(a__prod(mark(x0), false), mark(x2)), MARK(prod(x0, false))) A__ADD(s(prod(fact(z0), x1)), x2) -> c3(A__ADD(a__prod(a__fact(mark(z0)), mark(x1)), mark(x2)), MARK(prod(fact(z0), x1))) A__ADD(s(prod(if(z0, z1, z2), x1)), x2) -> c3(A__ADD(a__prod(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(prod(if(z0, z1, z2), x1))) A__ADD(s(prod(zero(z0), x1)), x2) -> c3(A__ADD(a__prod(a__zero(mark(z0)), mark(x1)), mark(x2)), MARK(prod(zero(z0), x1))) A__ADD(s(prod(prod(z0, z1), x1)), x2) -> c3(A__ADD(a__prod(a__prod(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(prod(prod(z0, z1), x1))) A__ADD(s(prod(p(z0), x1)), x2) -> c3(A__ADD(a__prod(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(prod(p(z0), x1))) A__ADD(s(prod(add(z0, z1), x1)), x2) -> c3(A__ADD(a__prod(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(prod(add(z0, z1), x1))) A__ADD(s(prod(s(z0), x1)), x2) -> c3(A__ADD(a__prod(s(mark(z0)), mark(x1)), mark(x2)), MARK(prod(s(z0), x1))) A__ADD(s(prod(0, x1)), x2) -> c3(A__ADD(a__prod(0, mark(x1)), mark(x2)), MARK(prod(0, x1))) A__ADD(s(prod(true, x1)), x2) -> c3(A__ADD(a__prod(true, mark(x1)), mark(x2)), MARK(prod(true, x1))) A__ADD(s(prod(false, x1)), x2) -> c3(A__ADD(a__prod(false, mark(x1)), mark(x2)), MARK(prod(false, x1))) A__ADD(s(prod(x0, x1)), x2) -> c3(MARK(prod(x0, x1))) A__ADD(s(p(fact(z0))), x1) -> c3(A__ADD(a__p(a__fact(mark(z0))), mark(x1)), MARK(p(fact(z0)))) A__ADD(s(p(if(z0, z1, z2))), x1) -> c3(A__ADD(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2)))) A__ADD(s(p(zero(z0))), x1) -> c3(A__ADD(a__p(a__zero(mark(z0))), mark(x1)), MARK(p(zero(z0)))) A__ADD(s(p(prod(z0, z1))), x1) -> c3(A__ADD(a__p(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(p(prod(z0, z1)))) A__ADD(s(p(p(z0))), x1) -> c3(A__ADD(a__p(a__p(mark(z0))), mark(x1)), MARK(p(p(z0)))) A__ADD(s(p(add(z0, z1))), x1) -> c3(A__ADD(a__p(a__add(mark(z0), mark(z1))), mark(x1)), MARK(p(add(z0, z1)))) A__ADD(s(p(s(z0))), x1) -> c3(A__ADD(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0)))) A__ADD(s(p(x0)), x1) -> c3(MARK(p(x0))) A__ADD(s(p(0)), x1) -> c3(A__ADD(a__p(0), mark(x1))) A__ADD(s(p(true)), x1) -> c3(A__ADD(a__p(true), mark(x1))) A__ADD(s(p(false)), x1) -> c3(A__ADD(a__p(false), mark(x1))) A__ADD(s(add(x0, fact(z0))), x2) -> c3(A__ADD(a__add(mark(x0), a__fact(mark(z0))), mark(x2)), MARK(add(x0, fact(z0)))) A__ADD(s(add(x0, if(z0, z1, z2))), x2) -> c3(A__ADD(a__add(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(add(x0, if(z0, z1, z2)))) A__ADD(s(add(x0, zero(z0))), x2) -> c3(A__ADD(a__add(mark(x0), a__zero(mark(z0))), mark(x2)), MARK(add(x0, zero(z0)))) A__ADD(s(add(x0, prod(z0, z1))), x2) -> c3(A__ADD(a__add(mark(x0), a__prod(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, prod(z0, z1)))) A__ADD(s(add(x0, p(z0))), x2) -> c3(A__ADD(a__add(mark(x0), a__p(mark(z0))), mark(x2)), MARK(add(x0, p(z0)))) A__ADD(s(add(x0, add(z0, z1))), x2) -> c3(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, add(z0, z1)))) A__ADD(s(add(x0, s(z0))), x2) -> c3(A__ADD(a__add(mark(x0), s(mark(z0))), mark(x2)), MARK(add(x0, s(z0)))) A__ADD(s(add(x0, 0)), x2) -> c3(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(add(x0, 0))) A__ADD(s(add(x0, true)), x2) -> c3(A__ADD(a__add(mark(x0), true), mark(x2)), MARK(add(x0, true))) A__ADD(s(add(x0, false)), x2) -> c3(A__ADD(a__add(mark(x0), false), mark(x2)), MARK(add(x0, false))) A__ADD(s(add(fact(z0), x1)), x2) -> c3(A__ADD(a__add(a__fact(mark(z0)), mark(x1)), mark(x2)), MARK(add(fact(z0), x1))) A__ADD(s(add(if(z0, z1, z2), x1)), x2) -> c3(A__ADD(a__add(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(add(if(z0, z1, z2), x1))) A__ADD(s(add(zero(z0), x1)), x2) -> c3(A__ADD(a__add(a__zero(mark(z0)), mark(x1)), mark(x2)), MARK(add(zero(z0), x1))) A__ADD(s(add(prod(z0, z1), x1)), x2) -> c3(A__ADD(a__add(a__prod(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(prod(z0, z1), x1))) A__ADD(s(add(p(z0), x1)), x2) -> c3(A__ADD(a__add(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(add(p(z0), x1))) A__ADD(s(add(add(z0, z1), x1)), x2) -> c3(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(add(z0, z1), x1))) A__ADD(s(add(s(z0), x1)), x2) -> c3(A__ADD(a__add(s(mark(z0)), mark(x1)), mark(x2)), MARK(add(s(z0), x1))) A__ADD(s(add(0, x1)), x2) -> c3(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(add(0, x1))) A__ADD(s(add(true, x1)), x2) -> c3(A__ADD(a__add(true, mark(x1)), mark(x2)), MARK(add(true, x1))) A__ADD(s(add(false, x1)), x2) -> c3(A__ADD(a__add(false, mark(x1)), mark(x2)), MARK(add(false, x1))) A__ADD(s(add(x0, x1)), x2) -> c3(MARK(add(x0, x1))) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__PROD_2, A__FACT_1 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c27_1, c21_1, c3_2, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1, c24_2, c25_2, c25_1, c26_2, c26_1, c_2, c_1 ---------------------------------------- (209) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__ADD(s(s(z0)), x1) -> c3(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) by A__ADD(s(s(x0)), fact(z0)) -> c3(A__ADD(s(mark(x0)), a__fact(mark(z0))), MARK(s(x0))) A__ADD(s(s(x0)), if(z0, z1, z2)) -> c3(A__ADD(s(mark(x0)), a__if(mark(z0), z1, z2)), MARK(s(x0))) A__ADD(s(s(x0)), zero(z0)) -> c3(A__ADD(s(mark(x0)), a__zero(mark(z0))), MARK(s(x0))) A__ADD(s(s(x0)), prod(z0, z1)) -> c3(A__ADD(s(mark(x0)), a__prod(mark(z0), mark(z1))), MARK(s(x0))) A__ADD(s(s(x0)), p(z0)) -> c3(A__ADD(s(mark(x0)), a__p(mark(z0))), MARK(s(x0))) A__ADD(s(s(x0)), add(z0, z1)) -> c3(A__ADD(s(mark(x0)), a__add(mark(z0), mark(z1))), MARK(s(x0))) A__ADD(s(s(x0)), s(z0)) -> c3(A__ADD(s(mark(x0)), s(mark(z0))), MARK(s(x0))) A__ADD(s(s(x0)), 0) -> c3(A__ADD(s(mark(x0)), 0), MARK(s(x0))) A__ADD(s(s(x0)), true) -> c3(A__ADD(s(mark(x0)), true), MARK(s(x0))) A__ADD(s(s(x0)), false) -> c3(A__ADD(s(mark(x0)), false), MARK(s(x0))) A__ADD(s(s(fact(z0))), x1) -> c3(A__ADD(s(a__fact(mark(z0))), mark(x1)), MARK(s(fact(z0)))) A__ADD(s(s(if(z0, z1, z2))), x1) -> c3(A__ADD(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(s(if(z0, z1, z2)))) A__ADD(s(s(zero(z0))), x1) -> c3(A__ADD(s(a__zero(mark(z0))), mark(x1)), MARK(s(zero(z0)))) A__ADD(s(s(prod(z0, z1))), x1) -> c3(A__ADD(s(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(s(prod(z0, z1)))) A__ADD(s(s(p(z0))), x1) -> c3(A__ADD(s(a__p(mark(z0))), mark(x1)), MARK(s(p(z0)))) A__ADD(s(s(add(z0, z1))), x1) -> c3(A__ADD(s(a__add(mark(z0), mark(z1))), mark(x1)), MARK(s(add(z0, z1)))) A__ADD(s(s(s(z0))), x1) -> c3(A__ADD(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__ADD(s(s(0)), x1) -> c3(A__ADD(s(0), mark(x1)), MARK(s(0))) A__ADD(s(s(true)), x1) -> c3(A__ADD(s(true), mark(x1)), MARK(s(true))) A__ADD(s(s(false)), x1) -> c3(A__ADD(s(false), mark(x1)), MARK(s(false))) A__ADD(s(s(x0)), x1) -> c3(MARK(s(x0))) ---------------------------------------- (210) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1)))) A__ADD(s(x0), prod(x1, x2)) -> c3(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) 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c3(A__ADD(a__if(false, x1, x2), mark(x3)), MARK(if(false, x1, x2))) A__ADD(s(if(x0, z1, z2)), x3) -> c3(MARK(if(x0, z1, z2))) A__ADD(s(if(0, x1, x2)), x3) -> c3(A__ADD(a__if(0, x1, x2), mark(x3))) A__ADD(s(zero(fact(z0))), x1) -> c3(A__ADD(a__zero(a__fact(mark(z0))), mark(x1)), MARK(zero(fact(z0)))) A__ADD(s(zero(if(z0, z1, z2))), x1) -> c3(A__ADD(a__zero(a__if(mark(z0), z1, z2)), mark(x1)), MARK(zero(if(z0, z1, z2)))) A__ADD(s(zero(zero(z0))), x1) -> c3(A__ADD(a__zero(a__zero(mark(z0))), mark(x1)), MARK(zero(zero(z0)))) A__ADD(s(zero(prod(z0, z1))), x1) -> c3(A__ADD(a__zero(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(zero(prod(z0, z1)))) A__ADD(s(zero(p(z0))), x1) -> c3(A__ADD(a__zero(a__p(mark(z0))), mark(x1)), MARK(zero(p(z0)))) A__ADD(s(zero(add(z0, z1))), x1) -> c3(A__ADD(a__zero(a__add(mark(z0), mark(z1))), mark(x1)), MARK(zero(add(z0, z1)))) A__ADD(s(zero(s(z0))), x1) -> c3(A__ADD(a__zero(s(mark(z0))), mark(x1)), MARK(zero(s(z0)))) A__ADD(s(zero(0)), x1) -> c3(A__ADD(a__zero(0), mark(x1)), MARK(zero(0))) A__ADD(s(zero(true)), x1) -> c3(A__ADD(a__zero(true), mark(x1)), MARK(zero(true))) A__ADD(s(zero(false)), x1) -> c3(A__ADD(a__zero(false), mark(x1)), MARK(zero(false))) A__ADD(s(zero(x0)), x1) -> c3(MARK(zero(x0))) A__ADD(s(prod(x0, fact(z0))), x2) -> c3(A__ADD(a__prod(mark(x0), a__fact(mark(z0))), mark(x2)), MARK(prod(x0, fact(z0)))) A__ADD(s(prod(x0, if(z0, z1, z2))), x2) -> c3(A__ADD(a__prod(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(prod(x0, if(z0, z1, z2)))) A__ADD(s(prod(x0, zero(z0))), x2) -> c3(A__ADD(a__prod(mark(x0), a__zero(mark(z0))), mark(x2)), MARK(prod(x0, zero(z0)))) A__ADD(s(prod(x0, prod(z0, z1))), x2) -> c3(A__ADD(a__prod(mark(x0), a__prod(mark(z0), mark(z1))), mark(x2)), MARK(prod(x0, prod(z0, z1)))) A__ADD(s(prod(x0, p(z0))), x2) -> c3(A__ADD(a__prod(mark(x0), a__p(mark(z0))), mark(x2)), MARK(prod(x0, p(z0)))) A__ADD(s(prod(x0, add(z0, z1))), x2) -> c3(A__ADD(a__prod(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(prod(x0, add(z0, z1)))) A__ADD(s(prod(x0, s(z0))), x2) -> c3(A__ADD(a__prod(mark(x0), s(mark(z0))), mark(x2)), MARK(prod(x0, s(z0)))) A__ADD(s(prod(x0, 0)), x2) -> c3(A__ADD(a__prod(mark(x0), 0), mark(x2)), MARK(prod(x0, 0))) A__ADD(s(prod(x0, true)), x2) -> c3(A__ADD(a__prod(mark(x0), true), mark(x2)), MARK(prod(x0, true))) A__ADD(s(prod(x0, false)), x2) -> c3(A__ADD(a__prod(mark(x0), false), mark(x2)), MARK(prod(x0, false))) A__ADD(s(prod(fact(z0), x1)), x2) -> c3(A__ADD(a__prod(a__fact(mark(z0)), mark(x1)), mark(x2)), MARK(prod(fact(z0), x1))) A__ADD(s(prod(if(z0, z1, z2), x1)), x2) -> c3(A__ADD(a__prod(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(prod(if(z0, z1, z2), x1))) A__ADD(s(prod(zero(z0), x1)), x2) -> c3(A__ADD(a__prod(a__zero(mark(z0)), mark(x1)), mark(x2)), MARK(prod(zero(z0), x1))) A__ADD(s(prod(prod(z0, z1), x1)), x2) -> c3(A__ADD(a__prod(a__prod(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(prod(prod(z0, z1), x1))) A__ADD(s(prod(p(z0), x1)), x2) -> c3(A__ADD(a__prod(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(prod(p(z0), x1))) A__ADD(s(prod(add(z0, z1), x1)), x2) -> c3(A__ADD(a__prod(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(prod(add(z0, z1), x1))) A__ADD(s(prod(s(z0), x1)), x2) -> c3(A__ADD(a__prod(s(mark(z0)), mark(x1)), mark(x2)), MARK(prod(s(z0), x1))) A__ADD(s(prod(0, x1)), x2) -> c3(A__ADD(a__prod(0, mark(x1)), mark(x2)), MARK(prod(0, x1))) A__ADD(s(prod(true, x1)), x2) -> c3(A__ADD(a__prod(true, mark(x1)), mark(x2)), MARK(prod(true, x1))) A__ADD(s(prod(false, x1)), x2) -> c3(A__ADD(a__prod(false, mark(x1)), mark(x2)), MARK(prod(false, x1))) A__ADD(s(prod(x0, x1)), x2) -> c3(MARK(prod(x0, x1))) A__ADD(s(p(fact(z0))), x1) -> c3(A__ADD(a__p(a__fact(mark(z0))), mark(x1)), MARK(p(fact(z0)))) A__ADD(s(p(if(z0, z1, z2))), x1) -> c3(A__ADD(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2)))) A__ADD(s(p(zero(z0))), x1) -> c3(A__ADD(a__p(a__zero(mark(z0))), mark(x1)), MARK(p(zero(z0)))) A__ADD(s(p(prod(z0, z1))), x1) -> c3(A__ADD(a__p(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(p(prod(z0, z1)))) A__ADD(s(p(p(z0))), x1) -> c3(A__ADD(a__p(a__p(mark(z0))), mark(x1)), MARK(p(p(z0)))) A__ADD(s(p(add(z0, z1))), x1) -> c3(A__ADD(a__p(a__add(mark(z0), mark(z1))), mark(x1)), MARK(p(add(z0, z1)))) A__ADD(s(p(s(z0))), x1) -> c3(A__ADD(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0)))) A__ADD(s(p(x0)), x1) -> c3(MARK(p(x0))) A__ADD(s(p(0)), x1) -> c3(A__ADD(a__p(0), mark(x1))) A__ADD(s(p(true)), x1) -> c3(A__ADD(a__p(true), mark(x1))) A__ADD(s(p(false)), x1) -> c3(A__ADD(a__p(false), mark(x1))) A__ADD(s(add(x0, fact(z0))), x2) -> c3(A__ADD(a__add(mark(x0), a__fact(mark(z0))), mark(x2)), MARK(add(x0, fact(z0)))) A__ADD(s(add(x0, if(z0, z1, z2))), x2) -> c3(A__ADD(a__add(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(add(x0, if(z0, z1, z2)))) A__ADD(s(add(x0, zero(z0))), x2) -> c3(A__ADD(a__add(mark(x0), a__zero(mark(z0))), mark(x2)), MARK(add(x0, zero(z0)))) A__ADD(s(add(x0, prod(z0, z1))), x2) -> c3(A__ADD(a__add(mark(x0), a__prod(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, prod(z0, z1)))) A__ADD(s(add(x0, p(z0))), x2) -> c3(A__ADD(a__add(mark(x0), a__p(mark(z0))), mark(x2)), MARK(add(x0, p(z0)))) A__ADD(s(add(x0, add(z0, z1))), x2) -> c3(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, add(z0, z1)))) A__ADD(s(add(x0, s(z0))), x2) -> c3(A__ADD(a__add(mark(x0), s(mark(z0))), mark(x2)), MARK(add(x0, s(z0)))) A__ADD(s(add(x0, 0)), x2) -> c3(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(add(x0, 0))) A__ADD(s(add(x0, true)), x2) -> c3(A__ADD(a__add(mark(x0), true), mark(x2)), MARK(add(x0, true))) A__ADD(s(add(x0, false)), x2) -> c3(A__ADD(a__add(mark(x0), false), mark(x2)), MARK(add(x0, false))) A__ADD(s(add(fact(z0), x1)), x2) -> c3(A__ADD(a__add(a__fact(mark(z0)), mark(x1)), mark(x2)), MARK(add(fact(z0), x1))) A__ADD(s(add(if(z0, z1, z2), x1)), x2) -> c3(A__ADD(a__add(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(add(if(z0, z1, z2), x1))) A__ADD(s(add(zero(z0), x1)), x2) -> c3(A__ADD(a__add(a__zero(mark(z0)), mark(x1)), mark(x2)), MARK(add(zero(z0), x1))) A__ADD(s(add(prod(z0, z1), x1)), x2) -> c3(A__ADD(a__add(a__prod(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(prod(z0, z1), x1))) A__ADD(s(add(p(z0), x1)), x2) -> c3(A__ADD(a__add(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(add(p(z0), x1))) A__ADD(s(add(add(z0, z1), x1)), x2) -> c3(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(add(z0, z1), x1))) A__ADD(s(add(s(z0), x1)), x2) -> c3(A__ADD(a__add(s(mark(z0)), mark(x1)), mark(x2)), MARK(add(s(z0), x1))) A__ADD(s(add(0, x1)), x2) -> c3(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(add(0, x1))) A__ADD(s(add(true, x1)), x2) -> c3(A__ADD(a__add(true, mark(x1)), mark(x2)), MARK(add(true, x1))) A__ADD(s(add(false, x1)), x2) -> c3(A__ADD(a__add(false, mark(x1)), mark(x2)), MARK(add(false, x1))) A__ADD(s(add(x0, x1)), x2) -> c3(MARK(add(x0, x1))) A__ADD(s(s(fact(z0))), x1) -> c3(A__ADD(s(a__fact(mark(z0))), mark(x1)), MARK(s(fact(z0)))) A__ADD(s(s(if(z0, z1, z2))), x1) -> c3(A__ADD(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(s(if(z0, z1, z2)))) A__ADD(s(s(zero(z0))), x1) -> c3(A__ADD(s(a__zero(mark(z0))), mark(x1)), MARK(s(zero(z0)))) A__ADD(s(s(prod(z0, z1))), x1) -> c3(A__ADD(s(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(s(prod(z0, z1)))) A__ADD(s(s(p(z0))), x1) -> c3(A__ADD(s(a__p(mark(z0))), mark(x1)), MARK(s(p(z0)))) A__ADD(s(s(add(z0, z1))), x1) -> c3(A__ADD(s(a__add(mark(z0), mark(z1))), mark(x1)), MARK(s(add(z0, z1)))) A__ADD(s(s(s(z0))), x1) -> c3(A__ADD(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__ADD(s(s(0)), x1) -> c3(A__ADD(s(0), mark(x1)), MARK(s(0))) A__ADD(s(s(true)), x1) -> c3(A__ADD(s(true), mark(x1)), MARK(s(true))) A__ADD(s(s(false)), x1) -> c3(A__ADD(s(false), mark(x1)), MARK(s(false))) A__ADD(s(s(x0)), x1) -> c3(MARK(s(x0))) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1)))) A__ADD(s(x0), prod(x1, x2)) -> c3(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), prod(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, p(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, s(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, 0)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), prod(x1, true)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(x0)) A__ADD(s(x0), prod(x1, false)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(x0)) A__ADD(s(x0), prod(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(p(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(add(z0, z1), 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MARK(zero(if(z0, z1, z2)))) A__ADD(s(zero(zero(z0))), x1) -> c3(A__ADD(a__zero(a__zero(mark(z0))), mark(x1)), MARK(zero(zero(z0)))) A__ADD(s(zero(prod(z0, z1))), x1) -> c3(A__ADD(a__zero(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(zero(prod(z0, z1)))) A__ADD(s(zero(p(z0))), x1) -> c3(A__ADD(a__zero(a__p(mark(z0))), mark(x1)), MARK(zero(p(z0)))) A__ADD(s(zero(add(z0, z1))), x1) -> c3(A__ADD(a__zero(a__add(mark(z0), mark(z1))), mark(x1)), MARK(zero(add(z0, z1)))) A__ADD(s(zero(s(z0))), x1) -> c3(A__ADD(a__zero(s(mark(z0))), mark(x1)), MARK(zero(s(z0)))) A__ADD(s(zero(0)), x1) -> c3(A__ADD(a__zero(0), mark(x1)), MARK(zero(0))) A__ADD(s(zero(true)), x1) -> c3(A__ADD(a__zero(true), mark(x1)), MARK(zero(true))) A__ADD(s(zero(false)), x1) -> c3(A__ADD(a__zero(false), mark(x1)), MARK(zero(false))) A__ADD(s(zero(x0)), x1) -> c3(MARK(zero(x0))) A__ADD(s(prod(x0, fact(z0))), x2) -> c3(A__ADD(a__prod(mark(x0), a__fact(mark(z0))), mark(x2)), MARK(prod(x0, fact(z0)))) A__ADD(s(prod(x0, if(z0, z1, z2))), x2) -> c3(A__ADD(a__prod(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(prod(x0, if(z0, z1, z2)))) A__ADD(s(prod(x0, zero(z0))), x2) -> c3(A__ADD(a__prod(mark(x0), a__zero(mark(z0))), mark(x2)), MARK(prod(x0, zero(z0)))) A__ADD(s(prod(x0, prod(z0, z1))), x2) -> c3(A__ADD(a__prod(mark(x0), a__prod(mark(z0), mark(z1))), mark(x2)), MARK(prod(x0, prod(z0, z1)))) A__ADD(s(prod(x0, p(z0))), x2) -> c3(A__ADD(a__prod(mark(x0), a__p(mark(z0))), mark(x2)), MARK(prod(x0, p(z0)))) A__ADD(s(prod(x0, add(z0, z1))), x2) -> c3(A__ADD(a__prod(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(prod(x0, add(z0, z1)))) A__ADD(s(prod(x0, s(z0))), x2) -> c3(A__ADD(a__prod(mark(x0), s(mark(z0))), mark(x2)), MARK(prod(x0, s(z0)))) A__ADD(s(prod(x0, 0)), x2) -> c3(A__ADD(a__prod(mark(x0), 0), mark(x2)), MARK(prod(x0, 0))) A__ADD(s(prod(x0, true)), x2) -> c3(A__ADD(a__prod(mark(x0), true), mark(x2)), MARK(prod(x0, true))) A__ADD(s(prod(x0, false)), x2) -> c3(A__ADD(a__prod(mark(x0), false), mark(x2)), MARK(prod(x0, false))) A__ADD(s(prod(fact(z0), x1)), x2) -> c3(A__ADD(a__prod(a__fact(mark(z0)), mark(x1)), mark(x2)), MARK(prod(fact(z0), x1))) A__ADD(s(prod(if(z0, z1, z2), x1)), x2) -> c3(A__ADD(a__prod(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(prod(if(z0, z1, z2), x1))) A__ADD(s(prod(zero(z0), x1)), x2) -> c3(A__ADD(a__prod(a__zero(mark(z0)), mark(x1)), mark(x2)), MARK(prod(zero(z0), x1))) A__ADD(s(prod(prod(z0, z1), x1)), x2) -> c3(A__ADD(a__prod(a__prod(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(prod(prod(z0, z1), x1))) A__ADD(s(prod(p(z0), x1)), x2) -> c3(A__ADD(a__prod(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(prod(p(z0), x1))) A__ADD(s(prod(add(z0, z1), x1)), x2) -> c3(A__ADD(a__prod(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(prod(add(z0, z1), x1))) A__ADD(s(prod(s(z0), x1)), x2) -> c3(A__ADD(a__prod(s(mark(z0)), mark(x1)), mark(x2)), MARK(prod(s(z0), x1))) A__ADD(s(prod(0, x1)), x2) -> c3(A__ADD(a__prod(0, mark(x1)), mark(x2)), MARK(prod(0, x1))) A__ADD(s(prod(true, x1)), x2) -> c3(A__ADD(a__prod(true, mark(x1)), mark(x2)), MARK(prod(true, x1))) A__ADD(s(prod(false, x1)), x2) -> c3(A__ADD(a__prod(false, mark(x1)), mark(x2)), MARK(prod(false, x1))) A__ADD(s(prod(x0, x1)), x2) -> c3(MARK(prod(x0, x1))) A__ADD(s(p(fact(z0))), x1) -> c3(A__ADD(a__p(a__fact(mark(z0))), mark(x1)), MARK(p(fact(z0)))) A__ADD(s(p(if(z0, z1, z2))), x1) -> c3(A__ADD(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2)))) A__ADD(s(p(zero(z0))), x1) -> c3(A__ADD(a__p(a__zero(mark(z0))), mark(x1)), MARK(p(zero(z0)))) A__ADD(s(p(prod(z0, z1))), x1) -> c3(A__ADD(a__p(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(p(prod(z0, z1)))) A__ADD(s(p(p(z0))), x1) -> c3(A__ADD(a__p(a__p(mark(z0))), mark(x1)), MARK(p(p(z0)))) A__ADD(s(p(add(z0, z1))), x1) -> c3(A__ADD(a__p(a__add(mark(z0), mark(z1))), mark(x1)), MARK(p(add(z0, z1)))) A__ADD(s(p(s(z0))), x1) -> c3(A__ADD(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0)))) A__ADD(s(p(x0)), x1) -> c3(MARK(p(x0))) A__ADD(s(p(0)), x1) -> c3(A__ADD(a__p(0), mark(x1))) A__ADD(s(p(true)), x1) -> c3(A__ADD(a__p(true), mark(x1))) A__ADD(s(p(false)), x1) -> c3(A__ADD(a__p(false), mark(x1))) A__ADD(s(add(x0, fact(z0))), x2) -> c3(A__ADD(a__add(mark(x0), a__fact(mark(z0))), mark(x2)), MARK(add(x0, fact(z0)))) A__ADD(s(add(x0, if(z0, z1, z2))), x2) -> c3(A__ADD(a__add(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(add(x0, if(z0, z1, z2)))) A__ADD(s(add(x0, zero(z0))), x2) -> c3(A__ADD(a__add(mark(x0), a__zero(mark(z0))), mark(x2)), MARK(add(x0, zero(z0)))) A__ADD(s(add(x0, prod(z0, z1))), x2) -> c3(A__ADD(a__add(mark(x0), a__prod(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, prod(z0, z1)))) A__ADD(s(add(x0, p(z0))), x2) -> c3(A__ADD(a__add(mark(x0), a__p(mark(z0))), mark(x2)), MARK(add(x0, p(z0)))) A__ADD(s(add(x0, add(z0, z1))), x2) -> c3(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, add(z0, z1)))) A__ADD(s(add(x0, s(z0))), x2) -> c3(A__ADD(a__add(mark(x0), s(mark(z0))), mark(x2)), MARK(add(x0, s(z0)))) A__ADD(s(add(x0, 0)), x2) -> c3(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(add(x0, 0))) A__ADD(s(add(x0, true)), x2) -> c3(A__ADD(a__add(mark(x0), true), mark(x2)), MARK(add(x0, true))) A__ADD(s(add(x0, false)), x2) -> c3(A__ADD(a__add(mark(x0), false), mark(x2)), MARK(add(x0, false))) A__ADD(s(add(fact(z0), x1)), x2) -> c3(A__ADD(a__add(a__fact(mark(z0)), mark(x1)), mark(x2)), MARK(add(fact(z0), x1))) A__ADD(s(add(if(z0, z1, z2), x1)), x2) -> c3(A__ADD(a__add(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(add(if(z0, z1, z2), x1))) A__ADD(s(add(zero(z0), x1)), x2) -> c3(A__ADD(a__add(a__zero(mark(z0)), mark(x1)), mark(x2)), MARK(add(zero(z0), x1))) A__ADD(s(add(prod(z0, z1), x1)), x2) -> c3(A__ADD(a__add(a__prod(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(prod(z0, z1), x1))) A__ADD(s(add(p(z0), x1)), x2) -> c3(A__ADD(a__add(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(add(p(z0), x1))) A__ADD(s(add(add(z0, z1), x1)), x2) -> c3(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(add(z0, z1), x1))) A__ADD(s(add(s(z0), x1)), x2) -> c3(A__ADD(a__add(s(mark(z0)), mark(x1)), mark(x2)), MARK(add(s(z0), x1))) A__ADD(s(add(0, x1)), x2) -> c3(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(add(0, x1))) A__ADD(s(add(true, x1)), x2) -> c3(A__ADD(a__add(true, mark(x1)), mark(x2)), MARK(add(true, x1))) A__ADD(s(add(false, x1)), x2) -> c3(A__ADD(a__add(false, mark(x1)), mark(x2)), MARK(add(false, x1))) A__ADD(s(add(x0, x1)), x2) -> c3(MARK(add(x0, x1))) A__ADD(s(s(fact(z0))), x1) -> c3(A__ADD(s(a__fact(mark(z0))), mark(x1)), MARK(s(fact(z0)))) A__ADD(s(s(if(z0, z1, z2))), x1) -> c3(A__ADD(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(s(if(z0, z1, z2)))) A__ADD(s(s(zero(z0))), x1) -> c3(A__ADD(s(a__zero(mark(z0))), mark(x1)), MARK(s(zero(z0)))) A__ADD(s(s(prod(z0, z1))), x1) -> c3(A__ADD(s(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(s(prod(z0, z1)))) A__ADD(s(s(p(z0))), x1) -> c3(A__ADD(s(a__p(mark(z0))), mark(x1)), MARK(s(p(z0)))) A__ADD(s(s(add(z0, z1))), x1) -> c3(A__ADD(s(a__add(mark(z0), mark(z1))), mark(x1)), MARK(s(add(z0, z1)))) A__ADD(s(s(s(z0))), x1) -> c3(A__ADD(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__ADD(s(s(0)), x1) -> c3(A__ADD(s(0), mark(x1)), MARK(s(0))) A__ADD(s(s(true)), x1) -> c3(A__ADD(s(true), mark(x1)), MARK(s(true))) A__ADD(s(s(false)), x1) -> c3(A__ADD(s(false), mark(x1)), MARK(s(false))) A__ADD(s(s(x0)), x1) -> c3(MARK(s(x0))) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__PROD_2, A__FACT_1 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c27_1, c21_1, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1, c24_2, c25_2, c25_1, c26_2, c26_1, c_2, c_1, c3_2 ---------------------------------------- (211) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__ADD(s(x0), fact(z0)) -> c4(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) by A__ADD(s(x0), fact(x1)) -> c4(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(fact(x1))) A__ADD(s(x0), fact(x1)) -> c4(A__ADD(mark(x0), fact(mark(x1))), MARK(fact(x1))) A__ADD(s(x0), fact(fact(z0))) -> c4(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(fact(fact(z0)))) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c4(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(fact(if(z0, z1, z2)))) A__ADD(s(x0), fact(zero(z0))) -> c4(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(fact(zero(z0)))) A__ADD(s(x0), fact(prod(z0, z1))) -> c4(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(fact(prod(z0, z1)))) A__ADD(s(x0), fact(p(z0))) -> c4(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(fact(p(z0)))) A__ADD(s(x0), fact(add(z0, z1))) -> c4(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(fact(add(z0, z1)))) A__ADD(s(x0), fact(s(z0))) -> c4(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(fact(s(z0)))) A__ADD(s(x0), fact(0)) -> c4(A__ADD(mark(x0), a__fact(0)), MARK(fact(0))) A__ADD(s(x0), fact(true)) -> c4(A__ADD(mark(x0), a__fact(true)), MARK(fact(true))) A__ADD(s(x0), fact(false)) -> c4(A__ADD(mark(x0), a__fact(false)), MARK(fact(false))) A__ADD(s(fact(z0)), fact(x1)) -> c4(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c4(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(zero(z0)), fact(x1)) -> c4(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(p(z0)), fact(x1)) -> c4(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(add(z0, z1)), fact(x1)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(s(z0)), fact(x1)) -> c4(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(0), fact(x1)) -> c4(A__ADD(0, a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(true), fact(x1)) -> c4(A__ADD(true, a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(false), fact(x1)) -> c4(A__ADD(false, a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(x0), fact(x1)) -> c4(MARK(fact(x1))) ---------------------------------------- (212) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1)))) A__ADD(s(x0), prod(x1, x2)) -> c3(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), prod(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, p(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, s(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, 0)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), prod(x1, true)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(x0)) A__ADD(s(x0), prod(x1, false)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(x0)) A__ADD(s(x0), prod(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, 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A__ADD(s(p(prod(z0, z1))), x1) -> c3(A__ADD(a__p(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(p(prod(z0, z1)))) A__ADD(s(p(p(z0))), x1) -> c3(A__ADD(a__p(a__p(mark(z0))), mark(x1)), MARK(p(p(z0)))) A__ADD(s(p(add(z0, z1))), x1) -> c3(A__ADD(a__p(a__add(mark(z0), mark(z1))), mark(x1)), MARK(p(add(z0, z1)))) A__ADD(s(p(s(z0))), x1) -> c3(A__ADD(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0)))) A__ADD(s(p(x0)), x1) -> c3(MARK(p(x0))) A__ADD(s(p(0)), x1) -> c3(A__ADD(a__p(0), mark(x1))) A__ADD(s(p(true)), x1) -> c3(A__ADD(a__p(true), mark(x1))) A__ADD(s(p(false)), x1) -> c3(A__ADD(a__p(false), mark(x1))) A__ADD(s(add(x0, fact(z0))), x2) -> c3(A__ADD(a__add(mark(x0), a__fact(mark(z0))), mark(x2)), MARK(add(x0, fact(z0)))) A__ADD(s(add(x0, if(z0, z1, z2))), x2) -> c3(A__ADD(a__add(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(add(x0, if(z0, z1, z2)))) A__ADD(s(add(x0, zero(z0))), x2) -> c3(A__ADD(a__add(mark(x0), a__zero(mark(z0))), mark(x2)), MARK(add(x0, zero(z0)))) A__ADD(s(add(x0, 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c3(A__ADD(s(a__fact(mark(z0))), mark(x1)), MARK(s(fact(z0)))) A__ADD(s(s(if(z0, z1, z2))), x1) -> c3(A__ADD(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(s(if(z0, z1, z2)))) A__ADD(s(s(zero(z0))), x1) -> c3(A__ADD(s(a__zero(mark(z0))), mark(x1)), MARK(s(zero(z0)))) A__ADD(s(s(prod(z0, z1))), x1) -> c3(A__ADD(s(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(s(prod(z0, z1)))) A__ADD(s(s(p(z0))), x1) -> c3(A__ADD(s(a__p(mark(z0))), mark(x1)), MARK(s(p(z0)))) A__ADD(s(s(add(z0, z1))), x1) -> c3(A__ADD(s(a__add(mark(z0), mark(z1))), mark(x1)), MARK(s(add(z0, z1)))) A__ADD(s(s(s(z0))), x1) -> c3(A__ADD(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__ADD(s(s(0)), x1) -> c3(A__ADD(s(0), mark(x1)), MARK(s(0))) A__ADD(s(s(true)), x1) -> c3(A__ADD(s(true), mark(x1)), MARK(s(true))) A__ADD(s(s(false)), x1) -> c3(A__ADD(s(false), mark(x1)), MARK(s(false))) A__ADD(s(s(x0)), x1) -> c3(MARK(s(x0))) A__ADD(s(x0), fact(x1)) -> c4(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), 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a__fact(true)), MARK(fact(true))) A__ADD(s(x0), fact(false)) -> c4(A__ADD(mark(x0), a__fact(false)), MARK(fact(false))) A__ADD(s(fact(z0)), fact(x1)) -> c4(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c4(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(zero(z0)), fact(x1)) -> c4(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(p(z0)), fact(x1)) -> c4(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(add(z0, z1)), fact(x1)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(s(z0)), fact(x1)) -> c4(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(0), fact(x1)) -> c4(A__ADD(0, a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(true), fact(x1)) -> c4(A__ADD(true, a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(false), fact(x1)) -> c4(A__ADD(false, a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(x0), fact(x1)) -> c4(MARK(fact(x1))) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) 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add(0, x2)) -> c3(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) A__ADD(s(x0), add(true, x2)) -> c3(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(x0)) A__ADD(s(x0), add(false, x2)) -> c3(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), add(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), add(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), add(x1, x2)) -> c3(A__ADD(s(mark(z0)), 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A__ADD(s(if(z0, z1, z2)), s(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), s(x1)) -> c3(A__ADD(a__zero(mark(z0)), s(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), s(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), s(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), s(x1)) -> c3(A__ADD(a__p(mark(z0)), s(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), s(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), s(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), s(x1)) -> c3(A__ADD(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__ADD(s(0), s(x1)) -> c3(A__ADD(0, s(mark(x1)))) A__ADD(s(fact(z0)), 0) -> c3(A__ADD(a__fact(mark(z0)), 0), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), 0) -> c3(A__ADD(a__if(mark(z0), z1, z2), 0), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), 0) -> c3(A__ADD(a__zero(mark(z0)), 0), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), 0) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), 0), MARK(prod(z0, z1))) A__ADD(s(p(z0)), 0) -> c3(A__ADD(a__p(mark(z0)), 0), MARK(p(z0))) A__ADD(s(add(z0, z1)), 0) -> c3(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) A__ADD(s(s(z0)), 0) -> c3(A__ADD(s(mark(z0)), 0), MARK(s(z0))) A__ADD(s(0), 0) -> c3(A__ADD(0, 0)) A__ADD(s(fact(z0)), true) -> c3(A__ADD(a__fact(mark(z0)), true), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), true) -> c3(A__ADD(a__if(mark(z0), z1, z2), true), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), true) -> c3(A__ADD(a__zero(mark(z0)), true), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), true) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), true), MARK(prod(z0, z1))) A__ADD(s(p(z0)), true) -> c3(A__ADD(a__p(mark(z0)), true), MARK(p(z0))) A__ADD(s(add(z0, z1)), true) -> c3(A__ADD(a__add(mark(z0), mark(z1)), true), MARK(add(z0, z1))) A__ADD(s(s(z0)), true) -> c3(A__ADD(s(mark(z0)), true), MARK(s(z0))) A__ADD(s(0), true) -> c3(A__ADD(0, true)) A__ADD(s(fact(z0)), false) -> c3(A__ADD(a__fact(mark(z0)), false), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), false) -> c3(A__ADD(a__if(mark(z0), z1, z2), false), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), false) -> c3(A__ADD(a__zero(mark(z0)), false), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), false) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), false), MARK(prod(z0, z1))) A__ADD(s(p(z0)), false) -> c3(A__ADD(a__p(mark(z0)), false), MARK(p(z0))) A__ADD(s(add(z0, z1)), false) -> c3(A__ADD(a__add(mark(z0), mark(z1)), false), MARK(add(z0, z1))) A__ADD(s(s(z0)), false) -> c3(A__ADD(s(mark(z0)), false), MARK(s(z0))) A__ADD(s(0), false) -> c3(A__ADD(0, false)) A__ADD(s(fact(x0)), x1) -> c3(A__ADD(a__if(a__zero(mark(mark(x0))), s(0), prod(mark(x0), fact(p(mark(x0))))), mark(x1)), MARK(fact(x0))) A__ADD(s(fact(fact(z0))), x1) -> c3(A__ADD(a__fact(a__fact(mark(z0))), mark(x1)), MARK(fact(fact(z0)))) A__ADD(s(fact(if(z0, z1, z2))), x1) -> c3(A__ADD(a__fact(a__if(mark(z0), z1, z2)), mark(x1)), MARK(fact(if(z0, z1, z2)))) A__ADD(s(fact(zero(z0))), x1) -> c3(A__ADD(a__fact(a__zero(mark(z0))), mark(x1)), MARK(fact(zero(z0)))) A__ADD(s(fact(prod(z0, z1))), x1) -> c3(A__ADD(a__fact(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(fact(prod(z0, z1)))) A__ADD(s(fact(p(z0))), x1) -> c3(A__ADD(a__fact(a__p(mark(z0))), mark(x1)), MARK(fact(p(z0)))) A__ADD(s(fact(add(z0, z1))), x1) -> c3(A__ADD(a__fact(a__add(mark(z0), mark(z1))), mark(x1)), MARK(fact(add(z0, z1)))) A__ADD(s(fact(s(z0))), x1) -> c3(A__ADD(a__fact(s(mark(z0))), mark(x1)), MARK(fact(s(z0)))) A__ADD(s(fact(0)), x1) -> c3(A__ADD(a__fact(0), mark(x1)), MARK(fact(0))) A__ADD(s(fact(true)), x1) -> c3(A__ADD(a__fact(true), mark(x1)), MARK(fact(true))) A__ADD(s(fact(false)), x1) -> c3(A__ADD(a__fact(false), mark(x1)), MARK(fact(false))) A__ADD(s(fact(x0)), x1) -> c3(MARK(fact(x0))) A__ADD(s(if(fact(z0), x1, x2)), x3) -> c3(A__ADD(a__if(a__fact(mark(z0)), x1, x2), mark(x3)), MARK(if(fact(z0), x1, x2))) A__ADD(s(if(if(z0, z1, z2), x1, x2)), x3) -> c3(A__ADD(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(if(if(z0, z1, z2), x1, x2))) A__ADD(s(if(zero(z0), x1, x2)), x3) -> c3(A__ADD(a__if(a__zero(mark(z0)), x1, x2), mark(x3)), MARK(if(zero(z0), x1, x2))) A__ADD(s(if(prod(z0, z1), x1, x2)), x3) -> c3(A__ADD(a__if(a__prod(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(prod(z0, z1), x1, x2))) A__ADD(s(if(p(z0), x1, x2)), x3) -> c3(A__ADD(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(if(p(z0), x1, x2))) A__ADD(s(if(add(z0, z1), x1, x2)), x3) -> c3(A__ADD(a__if(a__add(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(add(z0, z1), x1, x2))) A__ADD(s(if(s(z0), x1, x2)), x3) -> c3(A__ADD(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(if(s(z0), x1, x2))) A__ADD(s(if(true, x1, x2)), x3) -> c3(A__ADD(a__if(true, x1, x2), mark(x3)), MARK(if(true, x1, x2))) A__ADD(s(if(false, x1, x2)), x3) -> c3(A__ADD(a__if(false, x1, x2), mark(x3)), MARK(if(false, x1, x2))) A__ADD(s(if(x0, z1, z2)), x3) -> c3(MARK(if(x0, z1, z2))) A__ADD(s(if(0, x1, x2)), x3) -> c3(A__ADD(a__if(0, x1, x2), mark(x3))) A__ADD(s(zero(fact(z0))), x1) -> c3(A__ADD(a__zero(a__fact(mark(z0))), mark(x1)), MARK(zero(fact(z0)))) A__ADD(s(zero(if(z0, z1, z2))), x1) -> c3(A__ADD(a__zero(a__if(mark(z0), z1, z2)), mark(x1)), MARK(zero(if(z0, z1, z2)))) A__ADD(s(zero(zero(z0))), x1) -> c3(A__ADD(a__zero(a__zero(mark(z0))), mark(x1)), MARK(zero(zero(z0)))) A__ADD(s(zero(prod(z0, z1))), x1) -> c3(A__ADD(a__zero(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(zero(prod(z0, z1)))) A__ADD(s(zero(p(z0))), x1) -> c3(A__ADD(a__zero(a__p(mark(z0))), mark(x1)), MARK(zero(p(z0)))) A__ADD(s(zero(add(z0, z1))), x1) -> c3(A__ADD(a__zero(a__add(mark(z0), mark(z1))), mark(x1)), MARK(zero(add(z0, z1)))) A__ADD(s(zero(s(z0))), x1) -> c3(A__ADD(a__zero(s(mark(z0))), mark(x1)), MARK(zero(s(z0)))) A__ADD(s(zero(0)), x1) -> c3(A__ADD(a__zero(0), mark(x1)), MARK(zero(0))) A__ADD(s(zero(true)), x1) -> c3(A__ADD(a__zero(true), mark(x1)), MARK(zero(true))) A__ADD(s(zero(false)), x1) -> c3(A__ADD(a__zero(false), mark(x1)), MARK(zero(false))) A__ADD(s(zero(x0)), x1) -> c3(MARK(zero(x0))) A__ADD(s(prod(x0, fact(z0))), x2) -> c3(A__ADD(a__prod(mark(x0), a__fact(mark(z0))), mark(x2)), MARK(prod(x0, fact(z0)))) A__ADD(s(prod(x0, if(z0, z1, z2))), x2) -> c3(A__ADD(a__prod(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(prod(x0, if(z0, z1, z2)))) A__ADD(s(prod(x0, zero(z0))), x2) -> c3(A__ADD(a__prod(mark(x0), a__zero(mark(z0))), mark(x2)), MARK(prod(x0, zero(z0)))) A__ADD(s(prod(x0, prod(z0, z1))), x2) -> c3(A__ADD(a__prod(mark(x0), a__prod(mark(z0), mark(z1))), mark(x2)), MARK(prod(x0, prod(z0, z1)))) A__ADD(s(prod(x0, p(z0))), x2) -> c3(A__ADD(a__prod(mark(x0), a__p(mark(z0))), mark(x2)), MARK(prod(x0, p(z0)))) A__ADD(s(prod(x0, add(z0, z1))), x2) -> c3(A__ADD(a__prod(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(prod(x0, add(z0, z1)))) A__ADD(s(prod(x0, s(z0))), x2) -> c3(A__ADD(a__prod(mark(x0), s(mark(z0))), mark(x2)), MARK(prod(x0, s(z0)))) A__ADD(s(prod(x0, 0)), x2) -> c3(A__ADD(a__prod(mark(x0), 0), mark(x2)), MARK(prod(x0, 0))) A__ADD(s(prod(x0, true)), x2) -> c3(A__ADD(a__prod(mark(x0), true), mark(x2)), MARK(prod(x0, true))) A__ADD(s(prod(x0, false)), x2) -> c3(A__ADD(a__prod(mark(x0), false), mark(x2)), MARK(prod(x0, false))) A__ADD(s(prod(fact(z0), x1)), x2) -> c3(A__ADD(a__prod(a__fact(mark(z0)), mark(x1)), mark(x2)), MARK(prod(fact(z0), x1))) A__ADD(s(prod(if(z0, z1, z2), x1)), x2) -> c3(A__ADD(a__prod(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(prod(if(z0, z1, z2), x1))) A__ADD(s(prod(zero(z0), x1)), x2) -> c3(A__ADD(a__prod(a__zero(mark(z0)), mark(x1)), mark(x2)), MARK(prod(zero(z0), x1))) A__ADD(s(prod(prod(z0, z1), x1)), x2) -> c3(A__ADD(a__prod(a__prod(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(prod(prod(z0, z1), x1))) A__ADD(s(prod(p(z0), x1)), x2) -> c3(A__ADD(a__prod(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(prod(p(z0), x1))) A__ADD(s(prod(add(z0, z1), x1)), x2) -> c3(A__ADD(a__prod(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(prod(add(z0, z1), x1))) A__ADD(s(prod(s(z0), x1)), x2) -> c3(A__ADD(a__prod(s(mark(z0)), mark(x1)), mark(x2)), MARK(prod(s(z0), x1))) A__ADD(s(prod(0, x1)), x2) -> c3(A__ADD(a__prod(0, mark(x1)), mark(x2)), MARK(prod(0, x1))) A__ADD(s(prod(true, x1)), x2) -> c3(A__ADD(a__prod(true, mark(x1)), mark(x2)), MARK(prod(true, x1))) A__ADD(s(prod(false, x1)), x2) -> c3(A__ADD(a__prod(false, mark(x1)), mark(x2)), MARK(prod(false, x1))) A__ADD(s(prod(x0, x1)), x2) -> c3(MARK(prod(x0, x1))) A__ADD(s(p(fact(z0))), x1) -> c3(A__ADD(a__p(a__fact(mark(z0))), mark(x1)), MARK(p(fact(z0)))) A__ADD(s(p(if(z0, z1, z2))), x1) -> c3(A__ADD(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2)))) A__ADD(s(p(zero(z0))), x1) -> c3(A__ADD(a__p(a__zero(mark(z0))), mark(x1)), MARK(p(zero(z0)))) A__ADD(s(p(prod(z0, z1))), x1) -> c3(A__ADD(a__p(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(p(prod(z0, z1)))) A__ADD(s(p(p(z0))), x1) -> c3(A__ADD(a__p(a__p(mark(z0))), mark(x1)), MARK(p(p(z0)))) A__ADD(s(p(add(z0, z1))), x1) -> c3(A__ADD(a__p(a__add(mark(z0), mark(z1))), mark(x1)), MARK(p(add(z0, z1)))) A__ADD(s(p(s(z0))), x1) -> c3(A__ADD(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0)))) A__ADD(s(p(x0)), x1) -> c3(MARK(p(x0))) A__ADD(s(p(0)), x1) -> c3(A__ADD(a__p(0), mark(x1))) A__ADD(s(p(true)), x1) -> c3(A__ADD(a__p(true), mark(x1))) A__ADD(s(p(false)), x1) -> c3(A__ADD(a__p(false), mark(x1))) A__ADD(s(add(x0, fact(z0))), x2) -> c3(A__ADD(a__add(mark(x0), a__fact(mark(z0))), mark(x2)), MARK(add(x0, fact(z0)))) A__ADD(s(add(x0, if(z0, z1, z2))), x2) -> c3(A__ADD(a__add(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(add(x0, if(z0, z1, z2)))) A__ADD(s(add(x0, zero(z0))), x2) -> c3(A__ADD(a__add(mark(x0), a__zero(mark(z0))), mark(x2)), MARK(add(x0, zero(z0)))) A__ADD(s(add(x0, prod(z0, z1))), x2) -> c3(A__ADD(a__add(mark(x0), a__prod(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, prod(z0, z1)))) A__ADD(s(add(x0, p(z0))), x2) -> c3(A__ADD(a__add(mark(x0), a__p(mark(z0))), mark(x2)), MARK(add(x0, p(z0)))) A__ADD(s(add(x0, add(z0, z1))), x2) -> c3(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, add(z0, z1)))) A__ADD(s(add(x0, s(z0))), x2) -> c3(A__ADD(a__add(mark(x0), s(mark(z0))), mark(x2)), MARK(add(x0, s(z0)))) A__ADD(s(add(x0, 0)), x2) -> c3(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(add(x0, 0))) A__ADD(s(add(x0, true)), x2) -> c3(A__ADD(a__add(mark(x0), true), mark(x2)), MARK(add(x0, true))) A__ADD(s(add(x0, false)), x2) -> c3(A__ADD(a__add(mark(x0), false), mark(x2)), MARK(add(x0, false))) A__ADD(s(add(fact(z0), x1)), x2) -> c3(A__ADD(a__add(a__fact(mark(z0)), mark(x1)), mark(x2)), MARK(add(fact(z0), x1))) A__ADD(s(add(if(z0, z1, z2), x1)), x2) -> c3(A__ADD(a__add(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(add(if(z0, z1, z2), x1))) A__ADD(s(add(zero(z0), x1)), x2) -> c3(A__ADD(a__add(a__zero(mark(z0)), mark(x1)), mark(x2)), MARK(add(zero(z0), x1))) A__ADD(s(add(prod(z0, z1), x1)), x2) -> c3(A__ADD(a__add(a__prod(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(prod(z0, z1), x1))) A__ADD(s(add(p(z0), x1)), x2) -> c3(A__ADD(a__add(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(add(p(z0), x1))) A__ADD(s(add(add(z0, z1), x1)), x2) -> c3(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(add(z0, z1), x1))) A__ADD(s(add(s(z0), x1)), x2) -> c3(A__ADD(a__add(s(mark(z0)), mark(x1)), mark(x2)), MARK(add(s(z0), x1))) A__ADD(s(add(0, x1)), x2) -> c3(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(add(0, x1))) A__ADD(s(add(true, x1)), x2) -> c3(A__ADD(a__add(true, mark(x1)), mark(x2)), MARK(add(true, x1))) A__ADD(s(add(false, x1)), x2) -> c3(A__ADD(a__add(false, mark(x1)), mark(x2)), MARK(add(false, x1))) A__ADD(s(add(x0, x1)), x2) -> c3(MARK(add(x0, x1))) A__ADD(s(s(fact(z0))), x1) -> c3(A__ADD(s(a__fact(mark(z0))), mark(x1)), MARK(s(fact(z0)))) A__ADD(s(s(if(z0, z1, z2))), x1) -> c3(A__ADD(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(s(if(z0, z1, z2)))) A__ADD(s(s(zero(z0))), x1) -> c3(A__ADD(s(a__zero(mark(z0))), mark(x1)), MARK(s(zero(z0)))) A__ADD(s(s(prod(z0, z1))), x1) -> c3(A__ADD(s(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(s(prod(z0, z1)))) A__ADD(s(s(p(z0))), x1) -> c3(A__ADD(s(a__p(mark(z0))), mark(x1)), MARK(s(p(z0)))) A__ADD(s(s(add(z0, z1))), x1) -> c3(A__ADD(s(a__add(mark(z0), mark(z1))), mark(x1)), MARK(s(add(z0, z1)))) A__ADD(s(s(s(z0))), x1) -> c3(A__ADD(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__ADD(s(s(0)), x1) -> c3(A__ADD(s(0), mark(x1)), MARK(s(0))) A__ADD(s(s(true)), x1) -> c3(A__ADD(s(true), mark(x1)), MARK(s(true))) A__ADD(s(s(false)), x1) -> c3(A__ADD(s(false), mark(x1)), MARK(s(false))) A__ADD(s(s(x0)), x1) -> c3(MARK(s(x0))) A__ADD(s(x0), fact(x1)) -> c4(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(fact(x1))) A__ADD(s(x0), fact(x1)) -> c4(A__ADD(mark(x0), fact(mark(x1))), MARK(fact(x1))) A__ADD(s(x0), fact(fact(z0))) -> c4(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(fact(fact(z0)))) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c4(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(fact(if(z0, z1, z2)))) A__ADD(s(x0), fact(zero(z0))) -> c4(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(fact(zero(z0)))) A__ADD(s(x0), fact(prod(z0, z1))) -> c4(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(fact(prod(z0, z1)))) A__ADD(s(x0), fact(p(z0))) -> c4(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(fact(p(z0)))) A__ADD(s(x0), fact(add(z0, z1))) -> c4(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(fact(add(z0, z1)))) A__ADD(s(x0), fact(s(z0))) -> c4(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(fact(s(z0)))) A__ADD(s(x0), fact(0)) -> c4(A__ADD(mark(x0), a__fact(0)), MARK(fact(0))) A__ADD(s(x0), fact(true)) -> c4(A__ADD(mark(x0), a__fact(true)), MARK(fact(true))) A__ADD(s(x0), fact(false)) -> c4(A__ADD(mark(x0), a__fact(false)), MARK(fact(false))) A__ADD(s(fact(z0)), fact(x1)) -> c4(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c4(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(zero(z0)), fact(x1)) -> c4(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(p(z0)), fact(x1)) -> c4(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(add(z0, z1)), fact(x1)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(s(z0)), fact(x1)) -> c4(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(0), fact(x1)) -> c4(A__ADD(0, a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(true), fact(x1)) -> c4(A__ADD(true, a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(false), fact(x1)) -> c4(A__ADD(false, a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(x0), fact(x1)) -> c4(MARK(fact(x1))) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__PROD_2, A__FACT_1 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c27_1, c21_1, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1, c24_2, c25_2, c25_1, c26_2, c26_1, c_2, c_1, c3_2 ---------------------------------------- (213) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (214) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1)))) A__ADD(s(x0), prod(x1, x2)) -> c3(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), prod(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, p(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, s(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, 0)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), prod(x1, true)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(x0)) A__ADD(s(x0), prod(x1, false)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(x0)) A__ADD(s(x0), prod(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(p(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(0, x2)) -> c3(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(true, x2)) -> c3(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(false, x2)) -> c3(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), prod(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> 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x2) -> c3(A__ADD(a__prod(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(prod(p(z0), x1))) A__ADD(s(prod(add(z0, z1), x1)), x2) -> c3(A__ADD(a__prod(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(prod(add(z0, z1), x1))) A__ADD(s(prod(s(z0), x1)), x2) -> c3(A__ADD(a__prod(s(mark(z0)), mark(x1)), mark(x2)), MARK(prod(s(z0), x1))) A__ADD(s(prod(0, x1)), x2) -> c3(A__ADD(a__prod(0, mark(x1)), mark(x2)), MARK(prod(0, x1))) A__ADD(s(prod(true, x1)), x2) -> c3(A__ADD(a__prod(true, mark(x1)), mark(x2)), MARK(prod(true, x1))) A__ADD(s(prod(false, x1)), x2) -> c3(A__ADD(a__prod(false, mark(x1)), mark(x2)), MARK(prod(false, x1))) A__ADD(s(prod(x0, x1)), x2) -> c3(MARK(prod(x0, x1))) A__ADD(s(p(fact(z0))), x1) -> c3(A__ADD(a__p(a__fact(mark(z0))), mark(x1)), MARK(p(fact(z0)))) A__ADD(s(p(if(z0, z1, z2))), x1) -> c3(A__ADD(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2)))) A__ADD(s(p(zero(z0))), x1) -> c3(A__ADD(a__p(a__zero(mark(z0))), mark(x1)), MARK(p(zero(z0)))) A__ADD(s(p(prod(z0, z1))), x1) -> c3(A__ADD(a__p(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(p(prod(z0, z1)))) A__ADD(s(p(p(z0))), x1) -> c3(A__ADD(a__p(a__p(mark(z0))), mark(x1)), MARK(p(p(z0)))) A__ADD(s(p(add(z0, z1))), x1) -> c3(A__ADD(a__p(a__add(mark(z0), mark(z1))), mark(x1)), MARK(p(add(z0, z1)))) A__ADD(s(p(s(z0))), x1) -> c3(A__ADD(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0)))) A__ADD(s(p(x0)), x1) -> c3(MARK(p(x0))) A__ADD(s(p(0)), x1) -> c3(A__ADD(a__p(0), mark(x1))) A__ADD(s(p(true)), x1) -> c3(A__ADD(a__p(true), mark(x1))) A__ADD(s(p(false)), x1) -> c3(A__ADD(a__p(false), mark(x1))) A__ADD(s(add(x0, fact(z0))), x2) -> c3(A__ADD(a__add(mark(x0), a__fact(mark(z0))), mark(x2)), MARK(add(x0, fact(z0)))) A__ADD(s(add(x0, if(z0, z1, z2))), x2) -> c3(A__ADD(a__add(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(add(x0, if(z0, z1, z2)))) A__ADD(s(add(x0, zero(z0))), x2) -> c3(A__ADD(a__add(mark(x0), a__zero(mark(z0))), mark(x2)), MARK(add(x0, zero(z0)))) A__ADD(s(add(x0, prod(z0, z1))), x2) -> c3(A__ADD(a__add(mark(x0), a__prod(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, prod(z0, z1)))) A__ADD(s(add(x0, p(z0))), x2) -> c3(A__ADD(a__add(mark(x0), a__p(mark(z0))), mark(x2)), MARK(add(x0, p(z0)))) A__ADD(s(add(x0, add(z0, z1))), x2) -> c3(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, add(z0, z1)))) A__ADD(s(add(x0, s(z0))), x2) -> c3(A__ADD(a__add(mark(x0), s(mark(z0))), mark(x2)), MARK(add(x0, s(z0)))) A__ADD(s(add(x0, 0)), x2) -> c3(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(add(x0, 0))) A__ADD(s(add(x0, true)), x2) -> c3(A__ADD(a__add(mark(x0), true), mark(x2)), MARK(add(x0, true))) A__ADD(s(add(x0, false)), x2) -> c3(A__ADD(a__add(mark(x0), false), mark(x2)), MARK(add(x0, false))) A__ADD(s(add(fact(z0), x1)), x2) -> c3(A__ADD(a__add(a__fact(mark(z0)), mark(x1)), mark(x2)), MARK(add(fact(z0), x1))) A__ADD(s(add(if(z0, z1, z2), x1)), x2) -> c3(A__ADD(a__add(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(add(if(z0, z1, z2), x1))) A__ADD(s(add(zero(z0), x1)), x2) -> c3(A__ADD(a__add(a__zero(mark(z0)), mark(x1)), mark(x2)), MARK(add(zero(z0), x1))) A__ADD(s(add(prod(z0, z1), x1)), x2) -> c3(A__ADD(a__add(a__prod(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(prod(z0, z1), x1))) A__ADD(s(add(p(z0), x1)), x2) -> c3(A__ADD(a__add(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(add(p(z0), x1))) A__ADD(s(add(add(z0, z1), x1)), x2) -> c3(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(add(z0, z1), x1))) A__ADD(s(add(s(z0), x1)), x2) -> c3(A__ADD(a__add(s(mark(z0)), mark(x1)), mark(x2)), MARK(add(s(z0), x1))) A__ADD(s(add(0, x1)), x2) -> c3(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(add(0, x1))) A__ADD(s(add(true, x1)), x2) -> c3(A__ADD(a__add(true, mark(x1)), mark(x2)), MARK(add(true, x1))) A__ADD(s(add(false, x1)), x2) -> c3(A__ADD(a__add(false, mark(x1)), mark(x2)), MARK(add(false, x1))) A__ADD(s(add(x0, x1)), x2) -> c3(MARK(add(x0, x1))) A__ADD(s(s(fact(z0))), x1) -> c3(A__ADD(s(a__fact(mark(z0))), mark(x1)), MARK(s(fact(z0)))) A__ADD(s(s(if(z0, z1, z2))), x1) -> c3(A__ADD(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(s(if(z0, z1, z2)))) A__ADD(s(s(zero(z0))), x1) -> c3(A__ADD(s(a__zero(mark(z0))), mark(x1)), MARK(s(zero(z0)))) A__ADD(s(s(prod(z0, z1))), x1) -> c3(A__ADD(s(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(s(prod(z0, z1)))) A__ADD(s(s(p(z0))), x1) -> c3(A__ADD(s(a__p(mark(z0))), mark(x1)), MARK(s(p(z0)))) A__ADD(s(s(add(z0, z1))), x1) -> c3(A__ADD(s(a__add(mark(z0), mark(z1))), mark(x1)), MARK(s(add(z0, z1)))) A__ADD(s(s(s(z0))), x1) -> c3(A__ADD(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__ADD(s(s(0)), x1) -> c3(A__ADD(s(0), mark(x1)), MARK(s(0))) A__ADD(s(s(true)), x1) -> c3(A__ADD(s(true), mark(x1)), MARK(s(true))) A__ADD(s(s(false)), x1) -> c3(A__ADD(s(false), mark(x1)), MARK(s(false))) A__ADD(s(s(x0)), x1) -> c3(MARK(s(x0))) A__ADD(s(x0), fact(x1)) -> c4(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(fact(x1))) A__ADD(s(x0), fact(x1)) -> c4(A__ADD(mark(x0), fact(mark(x1))), MARK(fact(x1))) A__ADD(s(x0), fact(fact(z0))) -> c4(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(fact(fact(z0)))) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c4(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(fact(if(z0, z1, z2)))) A__ADD(s(x0), fact(zero(z0))) -> c4(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(fact(zero(z0)))) A__ADD(s(x0), fact(prod(z0, z1))) -> c4(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(fact(prod(z0, z1)))) A__ADD(s(x0), fact(p(z0))) -> c4(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(fact(p(z0)))) A__ADD(s(x0), fact(add(z0, z1))) -> c4(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(fact(add(z0, z1)))) A__ADD(s(x0), fact(s(z0))) -> c4(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(fact(s(z0)))) A__ADD(s(x0), fact(0)) -> c4(A__ADD(mark(x0), a__fact(0)), MARK(fact(0))) A__ADD(s(x0), fact(true)) -> c4(A__ADD(mark(x0), a__fact(true)), MARK(fact(true))) A__ADD(s(x0), fact(false)) -> c4(A__ADD(mark(x0), a__fact(false)), MARK(fact(false))) A__ADD(s(fact(z0)), fact(x1)) -> c4(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c4(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(zero(z0)), fact(x1)) -> c4(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(p(z0)), fact(x1)) -> c4(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(add(z0, z1)), fact(x1)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(s(z0)), fact(x1)) -> c4(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(0), fact(x1)) -> c4(A__ADD(0, a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(x0), fact(x1)) -> c4(MARK(fact(x1))) A__ADD(s(true), fact(x1)) -> c4(MARK(fact(x1))) A__ADD(s(false), fact(x1)) -> c4(MARK(fact(x1))) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> 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A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) 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c3(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(0, x2)) -> c3(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(true, x2)) -> c3(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(false, x2)) -> c3(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), prod(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), 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z1)), 0) -> c3(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) A__ADD(s(s(z0)), 0) -> c3(A__ADD(s(mark(z0)), 0), MARK(s(z0))) A__ADD(s(0), 0) -> c3(A__ADD(0, 0)) A__ADD(s(fact(z0)), true) -> c3(A__ADD(a__fact(mark(z0)), true), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), true) -> c3(A__ADD(a__if(mark(z0), z1, z2), true), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), true) -> c3(A__ADD(a__zero(mark(z0)), true), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), true) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), true), MARK(prod(z0, z1))) A__ADD(s(p(z0)), true) -> c3(A__ADD(a__p(mark(z0)), true), MARK(p(z0))) A__ADD(s(add(z0, z1)), true) -> c3(A__ADD(a__add(mark(z0), mark(z1)), true), MARK(add(z0, z1))) A__ADD(s(s(z0)), true) -> c3(A__ADD(s(mark(z0)), true), MARK(s(z0))) A__ADD(s(0), true) -> c3(A__ADD(0, true)) A__ADD(s(fact(z0)), false) -> c3(A__ADD(a__fact(mark(z0)), false), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), false) -> c3(A__ADD(a__if(mark(z0), z1, z2), false), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), false) -> c3(A__ADD(a__zero(mark(z0)), false), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), false) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), false), MARK(prod(z0, z1))) A__ADD(s(p(z0)), false) -> c3(A__ADD(a__p(mark(z0)), false), MARK(p(z0))) A__ADD(s(add(z0, z1)), false) -> c3(A__ADD(a__add(mark(z0), mark(z1)), false), MARK(add(z0, z1))) A__ADD(s(s(z0)), false) -> c3(A__ADD(s(mark(z0)), false), MARK(s(z0))) A__ADD(s(0), false) -> c3(A__ADD(0, false)) A__ADD(s(fact(x0)), x1) -> c3(A__ADD(a__if(a__zero(mark(mark(x0))), s(0), prod(mark(x0), fact(p(mark(x0))))), mark(x1)), MARK(fact(x0))) A__ADD(s(fact(fact(z0))), x1) -> c3(A__ADD(a__fact(a__fact(mark(z0))), mark(x1)), MARK(fact(fact(z0)))) A__ADD(s(fact(if(z0, z1, z2))), x1) -> c3(A__ADD(a__fact(a__if(mark(z0), z1, z2)), mark(x1)), MARK(fact(if(z0, z1, z2)))) A__ADD(s(fact(zero(z0))), x1) -> c3(A__ADD(a__fact(a__zero(mark(z0))), mark(x1)), MARK(fact(zero(z0)))) A__ADD(s(fact(prod(z0, z1))), x1) -> c3(A__ADD(a__fact(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(fact(prod(z0, z1)))) A__ADD(s(fact(p(z0))), x1) -> c3(A__ADD(a__fact(a__p(mark(z0))), mark(x1)), MARK(fact(p(z0)))) A__ADD(s(fact(add(z0, z1))), x1) -> c3(A__ADD(a__fact(a__add(mark(z0), mark(z1))), mark(x1)), MARK(fact(add(z0, z1)))) A__ADD(s(fact(s(z0))), x1) -> c3(A__ADD(a__fact(s(mark(z0))), mark(x1)), MARK(fact(s(z0)))) A__ADD(s(fact(0)), x1) -> c3(A__ADD(a__fact(0), mark(x1)), MARK(fact(0))) A__ADD(s(fact(true)), x1) -> c3(A__ADD(a__fact(true), mark(x1)), MARK(fact(true))) A__ADD(s(fact(false)), x1) -> c3(A__ADD(a__fact(false), mark(x1)), MARK(fact(false))) A__ADD(s(fact(x0)), x1) -> c3(MARK(fact(x0))) A__ADD(s(if(fact(z0), x1, x2)), x3) -> c3(A__ADD(a__if(a__fact(mark(z0)), x1, x2), mark(x3)), MARK(if(fact(z0), x1, x2))) A__ADD(s(if(if(z0, z1, z2), x1, x2)), x3) -> c3(A__ADD(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(if(if(z0, z1, z2), x1, x2))) A__ADD(s(if(zero(z0), x1, x2)), x3) -> c3(A__ADD(a__if(a__zero(mark(z0)), x1, x2), mark(x3)), MARK(if(zero(z0), x1, x2))) A__ADD(s(if(prod(z0, z1), x1, x2)), x3) -> c3(A__ADD(a__if(a__prod(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(prod(z0, z1), x1, x2))) A__ADD(s(if(p(z0), x1, x2)), x3) -> c3(A__ADD(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(if(p(z0), x1, x2))) A__ADD(s(if(add(z0, z1), x1, x2)), x3) -> c3(A__ADD(a__if(a__add(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(add(z0, z1), x1, x2))) A__ADD(s(if(s(z0), x1, x2)), x3) -> c3(A__ADD(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(if(s(z0), x1, x2))) A__ADD(s(if(true, x1, x2)), x3) -> c3(A__ADD(a__if(true, x1, x2), mark(x3)), MARK(if(true, x1, x2))) A__ADD(s(if(false, x1, x2)), x3) -> c3(A__ADD(a__if(false, x1, x2), mark(x3)), MARK(if(false, x1, x2))) A__ADD(s(if(x0, z1, z2)), x3) -> c3(MARK(if(x0, z1, z2))) A__ADD(s(if(0, x1, x2)), x3) -> c3(A__ADD(a__if(0, x1, x2), mark(x3))) A__ADD(s(zero(fact(z0))), x1) -> c3(A__ADD(a__zero(a__fact(mark(z0))), mark(x1)), MARK(zero(fact(z0)))) A__ADD(s(zero(if(z0, z1, z2))), x1) -> c3(A__ADD(a__zero(a__if(mark(z0), z1, z2)), mark(x1)), MARK(zero(if(z0, z1, z2)))) A__ADD(s(zero(zero(z0))), x1) -> c3(A__ADD(a__zero(a__zero(mark(z0))), mark(x1)), MARK(zero(zero(z0)))) A__ADD(s(zero(prod(z0, z1))), x1) -> c3(A__ADD(a__zero(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(zero(prod(z0, z1)))) A__ADD(s(zero(p(z0))), x1) -> c3(A__ADD(a__zero(a__p(mark(z0))), mark(x1)), MARK(zero(p(z0)))) A__ADD(s(zero(add(z0, z1))), x1) -> c3(A__ADD(a__zero(a__add(mark(z0), mark(z1))), mark(x1)), MARK(zero(add(z0, z1)))) A__ADD(s(zero(s(z0))), x1) -> c3(A__ADD(a__zero(s(mark(z0))), mark(x1)), MARK(zero(s(z0)))) A__ADD(s(zero(0)), x1) -> c3(A__ADD(a__zero(0), mark(x1)), MARK(zero(0))) A__ADD(s(zero(true)), x1) -> c3(A__ADD(a__zero(true), mark(x1)), MARK(zero(true))) A__ADD(s(zero(false)), x1) -> c3(A__ADD(a__zero(false), mark(x1)), MARK(zero(false))) A__ADD(s(zero(x0)), x1) -> c3(MARK(zero(x0))) A__ADD(s(prod(x0, fact(z0))), x2) 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c3(A__ADD(a__prod(mark(x0), true), mark(x2)), MARK(prod(x0, true))) A__ADD(s(prod(x0, false)), x2) -> c3(A__ADD(a__prod(mark(x0), false), mark(x2)), MARK(prod(x0, false))) A__ADD(s(prod(fact(z0), x1)), x2) -> c3(A__ADD(a__prod(a__fact(mark(z0)), mark(x1)), mark(x2)), MARK(prod(fact(z0), x1))) A__ADD(s(prod(if(z0, z1, z2), x1)), x2) -> c3(A__ADD(a__prod(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(prod(if(z0, z1, z2), x1))) A__ADD(s(prod(zero(z0), x1)), x2) -> c3(A__ADD(a__prod(a__zero(mark(z0)), mark(x1)), mark(x2)), MARK(prod(zero(z0), x1))) A__ADD(s(prod(prod(z0, z1), x1)), x2) -> c3(A__ADD(a__prod(a__prod(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(prod(prod(z0, z1), x1))) A__ADD(s(prod(p(z0), x1)), x2) -> c3(A__ADD(a__prod(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(prod(p(z0), x1))) A__ADD(s(prod(add(z0, z1), x1)), x2) -> c3(A__ADD(a__prod(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(prod(add(z0, z1), x1))) A__ADD(s(prod(s(z0), x1)), x2) -> c3(A__ADD(a__prod(s(mark(z0)), mark(x1)), mark(x2)), MARK(prod(s(z0), x1))) A__ADD(s(prod(0, x1)), x2) -> c3(A__ADD(a__prod(0, mark(x1)), mark(x2)), MARK(prod(0, x1))) A__ADD(s(prod(true, x1)), x2) -> c3(A__ADD(a__prod(true, mark(x1)), mark(x2)), MARK(prod(true, x1))) A__ADD(s(prod(false, x1)), x2) -> c3(A__ADD(a__prod(false, mark(x1)), mark(x2)), MARK(prod(false, x1))) A__ADD(s(prod(x0, x1)), x2) -> c3(MARK(prod(x0, x1))) A__ADD(s(p(fact(z0))), x1) -> c3(A__ADD(a__p(a__fact(mark(z0))), mark(x1)), MARK(p(fact(z0)))) A__ADD(s(p(if(z0, z1, z2))), x1) -> c3(A__ADD(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2)))) A__ADD(s(p(zero(z0))), x1) -> c3(A__ADD(a__p(a__zero(mark(z0))), mark(x1)), MARK(p(zero(z0)))) A__ADD(s(p(prod(z0, z1))), x1) -> c3(A__ADD(a__p(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(p(prod(z0, z1)))) A__ADD(s(p(p(z0))), x1) -> c3(A__ADD(a__p(a__p(mark(z0))), mark(x1)), MARK(p(p(z0)))) A__ADD(s(p(add(z0, z1))), x1) -> c3(A__ADD(a__p(a__add(mark(z0), mark(z1))), mark(x1)), MARK(p(add(z0, z1)))) A__ADD(s(p(s(z0))), x1) -> c3(A__ADD(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0)))) A__ADD(s(p(x0)), x1) -> c3(MARK(p(x0))) A__ADD(s(p(0)), x1) -> c3(A__ADD(a__p(0), mark(x1))) A__ADD(s(p(true)), x1) -> c3(A__ADD(a__p(true), mark(x1))) A__ADD(s(p(false)), x1) -> c3(A__ADD(a__p(false), mark(x1))) A__ADD(s(add(x0, fact(z0))), x2) -> c3(A__ADD(a__add(mark(x0), a__fact(mark(z0))), mark(x2)), MARK(add(x0, fact(z0)))) A__ADD(s(add(x0, if(z0, z1, z2))), x2) -> c3(A__ADD(a__add(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(add(x0, if(z0, z1, z2)))) A__ADD(s(add(x0, zero(z0))), x2) -> c3(A__ADD(a__add(mark(x0), a__zero(mark(z0))), mark(x2)), MARK(add(x0, zero(z0)))) A__ADD(s(add(x0, prod(z0, z1))), x2) -> c3(A__ADD(a__add(mark(x0), a__prod(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, prod(z0, z1)))) A__ADD(s(add(x0, p(z0))), x2) -> c3(A__ADD(a__add(mark(x0), a__p(mark(z0))), mark(x2)), MARK(add(x0, p(z0)))) A__ADD(s(add(x0, add(z0, z1))), x2) -> c3(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, add(z0, z1)))) A__ADD(s(add(x0, s(z0))), x2) -> c3(A__ADD(a__add(mark(x0), s(mark(z0))), mark(x2)), MARK(add(x0, s(z0)))) A__ADD(s(add(x0, 0)), x2) -> c3(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(add(x0, 0))) A__ADD(s(add(x0, true)), x2) -> c3(A__ADD(a__add(mark(x0), true), mark(x2)), MARK(add(x0, true))) A__ADD(s(add(x0, false)), x2) -> c3(A__ADD(a__add(mark(x0), false), mark(x2)), MARK(add(x0, false))) A__ADD(s(add(fact(z0), x1)), x2) -> c3(A__ADD(a__add(a__fact(mark(z0)), mark(x1)), mark(x2)), MARK(add(fact(z0), x1))) A__ADD(s(add(if(z0, z1, z2), x1)), x2) -> c3(A__ADD(a__add(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(add(if(z0, z1, z2), x1))) A__ADD(s(add(zero(z0), x1)), x2) -> c3(A__ADD(a__add(a__zero(mark(z0)), mark(x1)), mark(x2)), MARK(add(zero(z0), x1))) A__ADD(s(add(prod(z0, z1), x1)), x2) -> c3(A__ADD(a__add(a__prod(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(prod(z0, z1), x1))) A__ADD(s(add(p(z0), x1)), x2) -> c3(A__ADD(a__add(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(add(p(z0), x1))) A__ADD(s(add(add(z0, z1), x1)), x2) -> c3(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(add(z0, z1), x1))) A__ADD(s(add(s(z0), x1)), x2) -> c3(A__ADD(a__add(s(mark(z0)), mark(x1)), mark(x2)), MARK(add(s(z0), x1))) A__ADD(s(add(0, x1)), x2) -> c3(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(add(0, x1))) A__ADD(s(add(true, x1)), x2) -> c3(A__ADD(a__add(true, mark(x1)), mark(x2)), MARK(add(true, x1))) A__ADD(s(add(false, x1)), x2) -> c3(A__ADD(a__add(false, mark(x1)), mark(x2)), MARK(add(false, x1))) A__ADD(s(add(x0, x1)), x2) -> c3(MARK(add(x0, x1))) A__ADD(s(s(fact(z0))), x1) -> c3(A__ADD(s(a__fact(mark(z0))), mark(x1)), MARK(s(fact(z0)))) A__ADD(s(s(if(z0, z1, z2))), x1) -> c3(A__ADD(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(s(if(z0, z1, z2)))) A__ADD(s(s(zero(z0))), x1) -> c3(A__ADD(s(a__zero(mark(z0))), mark(x1)), MARK(s(zero(z0)))) A__ADD(s(s(prod(z0, z1))), x1) -> c3(A__ADD(s(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(s(prod(z0, z1)))) A__ADD(s(s(p(z0))), x1) -> c3(A__ADD(s(a__p(mark(z0))), mark(x1)), MARK(s(p(z0)))) A__ADD(s(s(add(z0, z1))), x1) -> c3(A__ADD(s(a__add(mark(z0), mark(z1))), mark(x1)), MARK(s(add(z0, z1)))) A__ADD(s(s(s(z0))), x1) -> c3(A__ADD(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__ADD(s(s(0)), x1) -> c3(A__ADD(s(0), mark(x1)), MARK(s(0))) A__ADD(s(s(true)), x1) -> c3(A__ADD(s(true), mark(x1)), MARK(s(true))) A__ADD(s(s(false)), x1) -> c3(A__ADD(s(false), mark(x1)), MARK(s(false))) A__ADD(s(s(x0)), x1) -> c3(MARK(s(x0))) A__ADD(s(x0), fact(x1)) -> c4(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(fact(x1))) A__ADD(s(x0), fact(x1)) -> c4(A__ADD(mark(x0), fact(mark(x1))), MARK(fact(x1))) A__ADD(s(x0), fact(fact(z0))) -> c4(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(fact(fact(z0)))) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c4(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(fact(if(z0, z1, z2)))) A__ADD(s(x0), fact(zero(z0))) -> c4(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(fact(zero(z0)))) A__ADD(s(x0), fact(prod(z0, z1))) -> c4(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(fact(prod(z0, z1)))) A__ADD(s(x0), fact(p(z0))) -> c4(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(fact(p(z0)))) A__ADD(s(x0), fact(add(z0, z1))) -> c4(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(fact(add(z0, z1)))) A__ADD(s(x0), fact(s(z0))) -> c4(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(fact(s(z0)))) A__ADD(s(x0), fact(0)) -> c4(A__ADD(mark(x0), a__fact(0)), MARK(fact(0))) A__ADD(s(x0), fact(true)) -> c4(A__ADD(mark(x0), a__fact(true)), MARK(fact(true))) A__ADD(s(x0), fact(false)) -> c4(A__ADD(mark(x0), a__fact(false)), MARK(fact(false))) A__ADD(s(fact(z0)), fact(x1)) -> c4(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c4(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(zero(z0)), fact(x1)) -> c4(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(p(z0)), fact(x1)) -> c4(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(add(z0, z1)), fact(x1)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(s(z0)), fact(x1)) -> c4(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(0), fact(x1)) -> c4(A__ADD(0, a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(x0), fact(x1)) -> c4(MARK(fact(x1))) A__ADD(s(true), fact(x1)) -> c4(MARK(fact(x1))) A__ADD(s(false), fact(x1)) -> c4(MARK(fact(x1))) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__PROD_2, A__FACT_1 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c27_1, c21_1, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1, c24_2, c25_2, c25_1, c26_2, c26_1, c_2, c_1, c3_2 ---------------------------------------- (215) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__ADD(s(x0), if(z0, z1, z2)) -> c4(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) by A__ADD(s(x0), if(x1, z1, z2)) -> c4(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(if(x1, z1, z2))) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(if(fact(z0), x2, x3))) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(if(if(z0, z1, z2), x2, x3))) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(if(zero(z0), x2, x3))) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(if(prod(z0, z1), x2, x3))) A__ADD(s(x0), if(p(z0), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(if(p(z0), x2, x3))) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(if(add(z0, z1), x2, x3))) A__ADD(s(x0), if(s(z0), x2, x3)) -> c4(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(if(s(z0), x2, x3))) A__ADD(s(x0), if(0, x2, x3)) -> c4(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(if(0, x2, x3))) A__ADD(s(x0), if(true, x2, x3)) -> c4(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(if(true, x2, x3))) A__ADD(s(x0), if(false, x2, x3)) -> c4(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(if(false, x2, x3))) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c4(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c4(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c4(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c4(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c4(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(0), if(x1, x2, x3)) -> c4(A__ADD(0, a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(true), if(x1, x2, x3)) -> c4(A__ADD(true, a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(false), if(x1, x2, x3)) -> c4(A__ADD(false, a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) ---------------------------------------- (216) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), 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fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1)))) A__ADD(s(x0), prod(x1, x2)) -> 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c3(A__ADD(a__p(a__fact(mark(z0))), mark(x1)), MARK(p(fact(z0)))) A__ADD(s(p(if(z0, z1, z2))), x1) -> c3(A__ADD(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2)))) A__ADD(s(p(zero(z0))), x1) -> c3(A__ADD(a__p(a__zero(mark(z0))), mark(x1)), MARK(p(zero(z0)))) A__ADD(s(p(prod(z0, z1))), x1) -> c3(A__ADD(a__p(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(p(prod(z0, z1)))) A__ADD(s(p(p(z0))), x1) -> c3(A__ADD(a__p(a__p(mark(z0))), mark(x1)), MARK(p(p(z0)))) A__ADD(s(p(add(z0, z1))), x1) -> c3(A__ADD(a__p(a__add(mark(z0), mark(z1))), mark(x1)), MARK(p(add(z0, z1)))) A__ADD(s(p(s(z0))), x1) -> c3(A__ADD(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0)))) A__ADD(s(p(x0)), x1) -> c3(MARK(p(x0))) A__ADD(s(p(0)), x1) -> c3(A__ADD(a__p(0), mark(x1))) A__ADD(s(p(true)), x1) -> c3(A__ADD(a__p(true), mark(x1))) A__ADD(s(p(false)), x1) -> c3(A__ADD(a__p(false), mark(x1))) A__ADD(s(add(x0, fact(z0))), x2) -> c3(A__ADD(a__add(mark(x0), a__fact(mark(z0))), mark(x2)), MARK(add(x0, fact(z0)))) A__ADD(s(add(x0, if(z0, z1, z2))), x2) -> c3(A__ADD(a__add(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(add(x0, if(z0, z1, z2)))) A__ADD(s(add(x0, zero(z0))), x2) -> c3(A__ADD(a__add(mark(x0), a__zero(mark(z0))), mark(x2)), MARK(add(x0, zero(z0)))) A__ADD(s(add(x0, prod(z0, z1))), x2) -> c3(A__ADD(a__add(mark(x0), a__prod(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, prod(z0, z1)))) A__ADD(s(add(x0, p(z0))), x2) -> c3(A__ADD(a__add(mark(x0), a__p(mark(z0))), mark(x2)), MARK(add(x0, p(z0)))) A__ADD(s(add(x0, add(z0, z1))), x2) -> c3(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, add(z0, z1)))) A__ADD(s(add(x0, s(z0))), x2) -> c3(A__ADD(a__add(mark(x0), s(mark(z0))), mark(x2)), MARK(add(x0, s(z0)))) A__ADD(s(add(x0, 0)), x2) -> c3(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(add(x0, 0))) A__ADD(s(add(x0, true)), x2) -> c3(A__ADD(a__add(mark(x0), true), mark(x2)), MARK(add(x0, true))) A__ADD(s(add(x0, false)), x2) -> c3(A__ADD(a__add(mark(x0), false), mark(x2)), MARK(add(x0, false))) A__ADD(s(add(fact(z0), x1)), x2) -> c3(A__ADD(a__add(a__fact(mark(z0)), mark(x1)), mark(x2)), MARK(add(fact(z0), x1))) A__ADD(s(add(if(z0, z1, z2), x1)), x2) -> c3(A__ADD(a__add(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(add(if(z0, z1, z2), x1))) A__ADD(s(add(zero(z0), x1)), x2) -> c3(A__ADD(a__add(a__zero(mark(z0)), mark(x1)), mark(x2)), MARK(add(zero(z0), x1))) A__ADD(s(add(prod(z0, z1), x1)), x2) -> c3(A__ADD(a__add(a__prod(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(prod(z0, z1), x1))) A__ADD(s(add(p(z0), x1)), x2) -> c3(A__ADD(a__add(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(add(p(z0), x1))) A__ADD(s(add(add(z0, z1), x1)), x2) -> c3(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(add(z0, z1), x1))) A__ADD(s(add(s(z0), x1)), x2) -> c3(A__ADD(a__add(s(mark(z0)), mark(x1)), mark(x2)), MARK(add(s(z0), x1))) A__ADD(s(add(0, x1)), x2) -> c3(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(add(0, x1))) A__ADD(s(add(true, x1)), x2) -> c3(A__ADD(a__add(true, mark(x1)), mark(x2)), MARK(add(true, x1))) A__ADD(s(add(false, x1)), x2) -> c3(A__ADD(a__add(false, mark(x1)), mark(x2)), MARK(add(false, x1))) A__ADD(s(add(x0, x1)), x2) -> c3(MARK(add(x0, x1))) A__ADD(s(s(fact(z0))), x1) -> c3(A__ADD(s(a__fact(mark(z0))), mark(x1)), MARK(s(fact(z0)))) A__ADD(s(s(if(z0, z1, z2))), x1) -> c3(A__ADD(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(s(if(z0, z1, z2)))) A__ADD(s(s(zero(z0))), x1) -> c3(A__ADD(s(a__zero(mark(z0))), mark(x1)), MARK(s(zero(z0)))) A__ADD(s(s(prod(z0, z1))), x1) -> c3(A__ADD(s(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(s(prod(z0, z1)))) A__ADD(s(s(p(z0))), x1) -> c3(A__ADD(s(a__p(mark(z0))), mark(x1)), MARK(s(p(z0)))) A__ADD(s(s(add(z0, z1))), x1) -> c3(A__ADD(s(a__add(mark(z0), mark(z1))), mark(x1)), MARK(s(add(z0, z1)))) A__ADD(s(s(s(z0))), x1) -> c3(A__ADD(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__ADD(s(s(0)), x1) -> c3(A__ADD(s(0), mark(x1)), MARK(s(0))) A__ADD(s(s(true)), x1) -> c3(A__ADD(s(true), mark(x1)), MARK(s(true))) A__ADD(s(s(false)), x1) -> c3(A__ADD(s(false), mark(x1)), MARK(s(false))) A__ADD(s(s(x0)), x1) -> c3(MARK(s(x0))) A__ADD(s(x0), fact(x1)) -> c4(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(fact(x1))) A__ADD(s(x0), fact(x1)) -> c4(A__ADD(mark(x0), fact(mark(x1))), MARK(fact(x1))) A__ADD(s(x0), fact(fact(z0))) -> c4(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(fact(fact(z0)))) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c4(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(fact(if(z0, z1, z2)))) A__ADD(s(x0), fact(zero(z0))) -> c4(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(fact(zero(z0)))) A__ADD(s(x0), fact(prod(z0, z1))) -> c4(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(fact(prod(z0, z1)))) A__ADD(s(x0), fact(p(z0))) -> c4(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(fact(p(z0)))) A__ADD(s(x0), fact(add(z0, z1))) -> c4(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(fact(add(z0, z1)))) A__ADD(s(x0), fact(s(z0))) -> c4(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(fact(s(z0)))) A__ADD(s(x0), fact(0)) -> c4(A__ADD(mark(x0), a__fact(0)), MARK(fact(0))) A__ADD(s(x0), fact(true)) -> c4(A__ADD(mark(x0), a__fact(true)), MARK(fact(true))) A__ADD(s(x0), fact(false)) -> c4(A__ADD(mark(x0), a__fact(false)), MARK(fact(false))) A__ADD(s(fact(z0)), fact(x1)) -> c4(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c4(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(zero(z0)), fact(x1)) -> c4(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(p(z0)), fact(x1)) -> c4(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(add(z0, z1)), fact(x1)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(s(z0)), fact(x1)) -> c4(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(0), fact(x1)) -> c4(A__ADD(0, a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(x0), fact(x1)) -> c4(MARK(fact(x1))) A__ADD(s(true), fact(x1)) -> c4(MARK(fact(x1))) A__ADD(s(false), fact(x1)) -> c4(MARK(fact(x1))) A__ADD(s(x0), if(x1, z1, z2)) -> c4(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(if(x1, z1, z2))) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(if(fact(z0), x2, x3))) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(if(if(z0, z1, z2), x2, x3))) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(if(zero(z0), x2, x3))) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(if(prod(z0, z1), x2, x3))) A__ADD(s(x0), if(p(z0), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(if(p(z0), x2, x3))) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(if(add(z0, z1), x2, x3))) A__ADD(s(x0), if(s(z0), x2, x3)) -> c4(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(if(s(z0), x2, x3))) A__ADD(s(x0), if(0, x2, x3)) -> c4(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(if(0, x2, x3))) A__ADD(s(x0), if(true, x2, x3)) -> c4(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(if(true, x2, x3))) A__ADD(s(x0), if(false, x2, x3)) -> c4(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(if(false, x2, x3))) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c4(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c4(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c4(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c4(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c4(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(0), if(x1, x2, x3)) -> c4(A__ADD(0, a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(true), if(x1, x2, x3)) -> c4(A__ADD(true, a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(false), if(x1, x2, x3)) -> c4(A__ADD(false, a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> 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c3(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), prod(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, p(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, s(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, 0)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), prod(x1, true)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(x0)) A__ADD(s(x0), prod(x1, false)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(x0)) A__ADD(s(x0), prod(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(p(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(0, x2)) -> c3(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(true, x2)) -> c3(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(false, x2)) -> c3(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), prod(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, 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a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1)))) A__ADD(s(x0), add(x1, x2)) -> c3(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), add(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), add(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, p(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, s(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, 0)) -> c3(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), add(x1, true)) -> c3(A__ADD(mark(x0), a__add(mark(x1), true)), MARK(x0)) A__ADD(s(x0), add(x1, false)) -> c3(A__ADD(mark(x0), a__add(mark(x1), false)), MARK(x0)) A__ADD(s(x0), add(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), add(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(p(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(s(z0), x2)) -> c3(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(0, x2)) -> c3(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) A__ADD(s(x0), add(true, x2)) -> c3(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(x0)) A__ADD(s(x0), add(false, x2)) -> c3(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), add(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), add(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), add(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__add(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), add(x1, x2)) -> c3(A__ADD(0, a__add(mark(x1), mark(x2)))) A__ADD(s(x0), s(fact(z0))) -> c3(A__ADD(mark(x0), s(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), s(zero(z0))) -> c3(A__ADD(mark(x0), s(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(prod(z0, z1))) -> c3(A__ADD(mark(x0), s(a__prod(mark(z0), 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c4(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(fact(add(z0, z1)))) A__ADD(s(x0), fact(s(z0))) -> c4(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(fact(s(z0)))) A__ADD(s(x0), fact(0)) -> c4(A__ADD(mark(x0), a__fact(0)), MARK(fact(0))) A__ADD(s(x0), fact(true)) -> c4(A__ADD(mark(x0), a__fact(true)), MARK(fact(true))) A__ADD(s(x0), fact(false)) -> c4(A__ADD(mark(x0), a__fact(false)), MARK(fact(false))) A__ADD(s(fact(z0)), fact(x1)) -> c4(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c4(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(zero(z0)), fact(x1)) -> c4(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(p(z0)), fact(x1)) -> c4(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(add(z0, z1)), fact(x1)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(s(z0)), fact(x1)) -> c4(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(0), fact(x1)) -> c4(A__ADD(0, a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(x0), fact(x1)) -> c4(MARK(fact(x1))) A__ADD(s(true), fact(x1)) -> c4(MARK(fact(x1))) A__ADD(s(false), fact(x1)) -> c4(MARK(fact(x1))) A__ADD(s(x0), if(x1, z1, z2)) -> c4(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(if(x1, z1, z2))) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(if(fact(z0), x2, x3))) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(if(if(z0, z1, z2), x2, x3))) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(if(zero(z0), x2, x3))) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(if(prod(z0, z1), x2, x3))) A__ADD(s(x0), if(p(z0), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(if(p(z0), x2, x3))) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(if(add(z0, z1), x2, x3))) A__ADD(s(x0), if(s(z0), x2, x3)) -> c4(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(if(s(z0), x2, x3))) A__ADD(s(x0), if(0, x2, x3)) -> c4(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(if(0, x2, x3))) A__ADD(s(x0), if(true, x2, x3)) -> c4(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(if(true, x2, x3))) A__ADD(s(x0), if(false, x2, x3)) -> c4(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(if(false, x2, x3))) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c4(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c4(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c4(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c4(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c4(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(0), if(x1, x2, x3)) -> c4(A__ADD(0, a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(true), if(x1, x2, x3)) -> c4(A__ADD(true, a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(false), if(x1, x2, x3)) -> c4(A__ADD(false, a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__PROD_2, A__FACT_1 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c27_1, c21_1, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1, c24_2, c25_2, c25_1, c26_2, c26_1, c_2, c_1, c3_2 ---------------------------------------- (217) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (218) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1)))) A__ADD(s(x0), prod(x1, x2)) -> c3(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), prod(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, p(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, s(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, 0)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), prod(x1, true)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(x0)) A__ADD(s(x0), prod(x1, false)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(x0)) A__ADD(s(x0), prod(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(p(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(0, x2)) -> c3(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(true, x2)) -> c3(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(false, x2)) -> c3(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), prod(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2)))) A__ADD(s(x0), p(x1)) -> c3(A__ADD(mark(x0), p(mark(x1))), MARK(x0)) A__ADD(s(x0), p(fact(z0))) -> c3(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), p(zero(z0))) -> c3(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(p(z0))) -> c3(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(add(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(s(z0))) -> c3(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(0)) -> c3(A__ADD(mark(x0), a__p(0)), MARK(x0)) A__ADD(s(x0), p(true)) -> c3(A__ADD(mark(x0), a__p(true)), MARK(x0)) A__ADD(s(x0), p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1)))) A__ADD(s(x0), add(x1, x2)) -> c3(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), add(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), add(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, p(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, s(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, 0)) -> c3(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), add(x1, true)) -> c3(A__ADD(mark(x0), a__add(mark(x1), true)), MARK(x0)) A__ADD(s(x0), add(x1, false)) -> c3(A__ADD(mark(x0), a__add(mark(x1), false)), MARK(x0)) A__ADD(s(x0), add(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), add(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(p(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(s(z0), x2)) -> c3(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(0, x2)) -> c3(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) A__ADD(s(x0), add(true, x2)) -> c3(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(x0)) A__ADD(s(x0), add(false, x2)) -> c3(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), add(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), add(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), 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fact(fact(z0))) -> c4(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(fact(fact(z0)))) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c4(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(fact(if(z0, z1, z2)))) A__ADD(s(x0), fact(zero(z0))) -> c4(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(fact(zero(z0)))) A__ADD(s(x0), fact(prod(z0, z1))) -> c4(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(fact(prod(z0, z1)))) A__ADD(s(x0), fact(p(z0))) -> c4(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(fact(p(z0)))) A__ADD(s(x0), fact(add(z0, z1))) -> c4(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(fact(add(z0, z1)))) A__ADD(s(x0), fact(s(z0))) -> c4(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(fact(s(z0)))) A__ADD(s(x0), fact(0)) -> c4(A__ADD(mark(x0), a__fact(0)), MARK(fact(0))) A__ADD(s(x0), fact(true)) -> c4(A__ADD(mark(x0), a__fact(true)), MARK(fact(true))) A__ADD(s(x0), fact(false)) -> c4(A__ADD(mark(x0), a__fact(false)), MARK(fact(false))) A__ADD(s(fact(z0)), fact(x1)) -> c4(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c4(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(zero(z0)), fact(x1)) -> c4(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(p(z0)), fact(x1)) -> c4(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(add(z0, z1)), fact(x1)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(s(z0)), fact(x1)) -> c4(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(0), fact(x1)) -> c4(A__ADD(0, a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(x0), fact(x1)) -> c4(MARK(fact(x1))) A__ADD(s(true), fact(x1)) -> c4(MARK(fact(x1))) A__ADD(s(false), fact(x1)) -> c4(MARK(fact(x1))) A__ADD(s(x0), if(x1, z1, z2)) -> c4(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(if(x1, z1, z2))) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(if(fact(z0), x2, x3))) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(if(if(z0, z1, z2), x2, x3))) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(if(zero(z0), x2, x3))) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(if(prod(z0, z1), x2, x3))) A__ADD(s(x0), if(p(z0), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(if(p(z0), x2, x3))) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(if(add(z0, z1), x2, x3))) A__ADD(s(x0), if(s(z0), x2, x3)) -> c4(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(if(s(z0), x2, x3))) A__ADD(s(x0), if(true, x2, x3)) -> c4(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(if(true, x2, x3))) A__ADD(s(x0), if(false, x2, x3)) -> c4(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(if(false, x2, x3))) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c4(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c4(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c4(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c4(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c4(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(0), if(x1, x2, x3)) -> c4(A__ADD(0, a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(x0), if(0, x2, x3)) -> c4(A__ADD(mark(x0), a__if(0, x2, x3))) A__ADD(s(true), if(x1, x2, x3)) -> c4(MARK(if(x1, x2, x3))) A__ADD(s(false), if(x1, x2, x3)) -> c4(MARK(if(x1, x2, x3))) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), 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MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, 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c3(A__ADD(a__if(a__zero(mark(z0)), x1, x2), mark(x3)), MARK(if(zero(z0), x1, x2))) A__ADD(s(if(prod(z0, z1), x1, x2)), x3) -> c3(A__ADD(a__if(a__prod(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(prod(z0, z1), x1, x2))) A__ADD(s(if(p(z0), x1, x2)), x3) -> c3(A__ADD(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(if(p(z0), x1, x2))) A__ADD(s(if(add(z0, z1), x1, x2)), x3) -> c3(A__ADD(a__if(a__add(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(add(z0, z1), x1, x2))) A__ADD(s(if(s(z0), x1, x2)), x3) -> c3(A__ADD(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(if(s(z0), x1, x2))) A__ADD(s(if(true, x1, x2)), x3) -> c3(A__ADD(a__if(true, x1, x2), mark(x3)), MARK(if(true, x1, x2))) A__ADD(s(if(false, x1, x2)), x3) -> c3(A__ADD(a__if(false, x1, x2), mark(x3)), MARK(if(false, x1, x2))) A__ADD(s(if(x0, z1, z2)), x3) -> c3(MARK(if(x0, z1, z2))) A__ADD(s(if(0, x1, x2)), x3) -> c3(A__ADD(a__if(0, x1, x2), mark(x3))) A__ADD(s(zero(fact(z0))), x1) -> c3(A__ADD(a__zero(a__fact(mark(z0))), mark(x1)), MARK(zero(fact(z0)))) A__ADD(s(zero(if(z0, z1, z2))), x1) -> c3(A__ADD(a__zero(a__if(mark(z0), z1, z2)), mark(x1)), MARK(zero(if(z0, z1, z2)))) A__ADD(s(zero(zero(z0))), x1) -> c3(A__ADD(a__zero(a__zero(mark(z0))), mark(x1)), MARK(zero(zero(z0)))) A__ADD(s(zero(prod(z0, z1))), x1) -> c3(A__ADD(a__zero(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(zero(prod(z0, z1)))) A__ADD(s(zero(p(z0))), x1) -> c3(A__ADD(a__zero(a__p(mark(z0))), mark(x1)), MARK(zero(p(z0)))) A__ADD(s(zero(add(z0, z1))), x1) -> c3(A__ADD(a__zero(a__add(mark(z0), mark(z1))), mark(x1)), MARK(zero(add(z0, z1)))) A__ADD(s(zero(s(z0))), x1) -> c3(A__ADD(a__zero(s(mark(z0))), mark(x1)), MARK(zero(s(z0)))) A__ADD(s(zero(0)), x1) -> c3(A__ADD(a__zero(0), mark(x1)), MARK(zero(0))) A__ADD(s(zero(true)), x1) -> c3(A__ADD(a__zero(true), mark(x1)), MARK(zero(true))) A__ADD(s(zero(false)), x1) -> c3(A__ADD(a__zero(false), mark(x1)), MARK(zero(false))) A__ADD(s(zero(x0)), x1) -> c3(MARK(zero(x0))) A__ADD(s(prod(x0, fact(z0))), x2) 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c3(A__ADD(a__prod(s(mark(z0)), mark(x1)), mark(x2)), MARK(prod(s(z0), x1))) A__ADD(s(prod(0, x1)), x2) -> c3(A__ADD(a__prod(0, mark(x1)), mark(x2)), MARK(prod(0, x1))) A__ADD(s(prod(true, x1)), x2) -> c3(A__ADD(a__prod(true, mark(x1)), mark(x2)), MARK(prod(true, x1))) A__ADD(s(prod(false, x1)), x2) -> c3(A__ADD(a__prod(false, mark(x1)), mark(x2)), MARK(prod(false, x1))) A__ADD(s(prod(x0, x1)), x2) -> c3(MARK(prod(x0, x1))) A__ADD(s(p(fact(z0))), x1) -> c3(A__ADD(a__p(a__fact(mark(z0))), mark(x1)), MARK(p(fact(z0)))) A__ADD(s(p(if(z0, z1, z2))), x1) -> c3(A__ADD(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2)))) A__ADD(s(p(zero(z0))), x1) -> c3(A__ADD(a__p(a__zero(mark(z0))), mark(x1)), MARK(p(zero(z0)))) A__ADD(s(p(prod(z0, z1))), x1) -> c3(A__ADD(a__p(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(p(prod(z0, z1)))) A__ADD(s(p(p(z0))), x1) -> c3(A__ADD(a__p(a__p(mark(z0))), mark(x1)), MARK(p(p(z0)))) A__ADD(s(p(add(z0, z1))), x1) -> c3(A__ADD(a__p(a__add(mark(z0), mark(z1))), mark(x1)), MARK(p(add(z0, z1)))) A__ADD(s(p(s(z0))), x1) -> c3(A__ADD(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0)))) A__ADD(s(p(x0)), x1) -> c3(MARK(p(x0))) A__ADD(s(p(0)), x1) -> c3(A__ADD(a__p(0), mark(x1))) A__ADD(s(p(true)), x1) -> c3(A__ADD(a__p(true), mark(x1))) A__ADD(s(p(false)), x1) -> c3(A__ADD(a__p(false), mark(x1))) A__ADD(s(add(x0, fact(z0))), x2) -> c3(A__ADD(a__add(mark(x0), a__fact(mark(z0))), mark(x2)), MARK(add(x0, fact(z0)))) A__ADD(s(add(x0, if(z0, z1, z2))), x2) -> c3(A__ADD(a__add(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(add(x0, if(z0, z1, z2)))) A__ADD(s(add(x0, zero(z0))), x2) -> c3(A__ADD(a__add(mark(x0), a__zero(mark(z0))), mark(x2)), MARK(add(x0, zero(z0)))) A__ADD(s(add(x0, prod(z0, z1))), x2) -> c3(A__ADD(a__add(mark(x0), a__prod(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, prod(z0, z1)))) A__ADD(s(add(x0, p(z0))), x2) -> c3(A__ADD(a__add(mark(x0), a__p(mark(z0))), mark(x2)), MARK(add(x0, p(z0)))) A__ADD(s(add(x0, add(z0, z1))), x2) -> c3(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, add(z0, z1)))) A__ADD(s(add(x0, s(z0))), x2) -> c3(A__ADD(a__add(mark(x0), s(mark(z0))), mark(x2)), MARK(add(x0, s(z0)))) A__ADD(s(add(x0, 0)), x2) -> c3(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(add(x0, 0))) A__ADD(s(add(x0, true)), x2) -> c3(A__ADD(a__add(mark(x0), true), mark(x2)), MARK(add(x0, true))) A__ADD(s(add(x0, false)), x2) -> c3(A__ADD(a__add(mark(x0), false), mark(x2)), MARK(add(x0, false))) A__ADD(s(add(fact(z0), x1)), x2) -> c3(A__ADD(a__add(a__fact(mark(z0)), mark(x1)), mark(x2)), MARK(add(fact(z0), x1))) A__ADD(s(add(if(z0, z1, z2), x1)), x2) -> c3(A__ADD(a__add(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(add(if(z0, z1, z2), x1))) A__ADD(s(add(zero(z0), x1)), x2) -> c3(A__ADD(a__add(a__zero(mark(z0)), mark(x1)), mark(x2)), MARK(add(zero(z0), x1))) A__ADD(s(add(prod(z0, z1), x1)), x2) -> c3(A__ADD(a__add(a__prod(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(prod(z0, z1), x1))) A__ADD(s(add(p(z0), x1)), x2) -> c3(A__ADD(a__add(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(add(p(z0), x1))) A__ADD(s(add(add(z0, z1), x1)), x2) -> c3(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(add(z0, z1), x1))) A__ADD(s(add(s(z0), x1)), x2) -> c3(A__ADD(a__add(s(mark(z0)), mark(x1)), mark(x2)), MARK(add(s(z0), x1))) A__ADD(s(add(0, x1)), x2) -> c3(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(add(0, x1))) A__ADD(s(add(true, x1)), x2) -> c3(A__ADD(a__add(true, mark(x1)), mark(x2)), MARK(add(true, x1))) A__ADD(s(add(false, x1)), x2) -> c3(A__ADD(a__add(false, mark(x1)), mark(x2)), MARK(add(false, x1))) A__ADD(s(add(x0, x1)), x2) -> c3(MARK(add(x0, x1))) A__ADD(s(s(fact(z0))), x1) -> c3(A__ADD(s(a__fact(mark(z0))), mark(x1)), MARK(s(fact(z0)))) A__ADD(s(s(if(z0, z1, z2))), x1) -> c3(A__ADD(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(s(if(z0, z1, z2)))) A__ADD(s(s(zero(z0))), x1) -> c3(A__ADD(s(a__zero(mark(z0))), mark(x1)), MARK(s(zero(z0)))) A__ADD(s(s(prod(z0, z1))), x1) -> c3(A__ADD(s(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(s(prod(z0, z1)))) A__ADD(s(s(p(z0))), x1) -> c3(A__ADD(s(a__p(mark(z0))), mark(x1)), MARK(s(p(z0)))) A__ADD(s(s(add(z0, z1))), x1) -> c3(A__ADD(s(a__add(mark(z0), mark(z1))), mark(x1)), MARK(s(add(z0, z1)))) A__ADD(s(s(s(z0))), x1) -> c3(A__ADD(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__ADD(s(s(0)), x1) -> c3(A__ADD(s(0), mark(x1)), MARK(s(0))) A__ADD(s(s(true)), x1) -> c3(A__ADD(s(true), mark(x1)), MARK(s(true))) A__ADD(s(s(false)), x1) -> c3(A__ADD(s(false), mark(x1)), MARK(s(false))) A__ADD(s(s(x0)), x1) -> c3(MARK(s(x0))) A__ADD(s(x0), fact(x1)) -> c4(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(fact(x1))) A__ADD(s(x0), fact(x1)) -> c4(A__ADD(mark(x0), fact(mark(x1))), MARK(fact(x1))) A__ADD(s(x0), fact(fact(z0))) -> c4(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(fact(fact(z0)))) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c4(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(fact(if(z0, z1, z2)))) A__ADD(s(x0), fact(zero(z0))) -> c4(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(fact(zero(z0)))) A__ADD(s(x0), fact(prod(z0, z1))) -> c4(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(fact(prod(z0, z1)))) A__ADD(s(x0), fact(p(z0))) -> c4(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(fact(p(z0)))) A__ADD(s(x0), fact(add(z0, z1))) -> c4(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(fact(add(z0, z1)))) A__ADD(s(x0), fact(s(z0))) -> c4(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(fact(s(z0)))) A__ADD(s(x0), fact(0)) -> c4(A__ADD(mark(x0), a__fact(0)), MARK(fact(0))) A__ADD(s(x0), fact(true)) -> c4(A__ADD(mark(x0), a__fact(true)), MARK(fact(true))) A__ADD(s(x0), fact(false)) -> c4(A__ADD(mark(x0), a__fact(false)), MARK(fact(false))) A__ADD(s(fact(z0)), fact(x1)) -> c4(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c4(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(zero(z0)), fact(x1)) -> c4(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(p(z0)), fact(x1)) -> c4(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(add(z0, z1)), fact(x1)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(s(z0)), fact(x1)) -> c4(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(0), fact(x1)) -> c4(A__ADD(0, a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(x0), fact(x1)) -> c4(MARK(fact(x1))) A__ADD(s(true), fact(x1)) -> c4(MARK(fact(x1))) A__ADD(s(false), fact(x1)) -> c4(MARK(fact(x1))) A__ADD(s(x0), if(x1, z1, z2)) -> c4(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(if(x1, z1, z2))) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(if(fact(z0), x2, x3))) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(if(if(z0, z1, z2), x2, x3))) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(if(zero(z0), x2, x3))) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(if(prod(z0, z1), x2, x3))) A__ADD(s(x0), if(p(z0), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(if(p(z0), x2, x3))) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(if(add(z0, z1), x2, x3))) A__ADD(s(x0), if(s(z0), x2, x3)) -> c4(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(if(s(z0), x2, x3))) A__ADD(s(x0), if(true, x2, x3)) -> c4(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(if(true, x2, x3))) A__ADD(s(x0), if(false, x2, x3)) -> c4(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(if(false, x2, x3))) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c4(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c4(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c4(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c4(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c4(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(0), if(x1, x2, x3)) -> c4(A__ADD(0, a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(x0), if(0, x2, x3)) -> c4(A__ADD(mark(x0), a__if(0, x2, x3))) A__ADD(s(true), if(x1, x2, x3)) -> c4(MARK(if(x1, x2, x3))) A__ADD(s(false), if(x1, x2, x3)) -> c4(MARK(if(x1, x2, x3))) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__PROD_2, A__FACT_1 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c27_1, c21_1, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1, c24_2, c25_2, c25_1, c26_2, c26_1, c_2, c_1, c3_2 ---------------------------------------- (219) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__ADD(s(x0), zero(z0)) -> c4(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) by A__ADD(s(x0), zero(x1)) -> c4(A__ADD(mark(x0), zero(mark(x1))), MARK(zero(x1))) A__ADD(s(x0), zero(fact(z0))) -> c4(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(zero(fact(z0)))) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c4(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(zero(if(z0, z1, z2)))) A__ADD(s(x0), zero(zero(z0))) -> c4(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(zero(zero(z0)))) A__ADD(s(x0), zero(prod(z0, z1))) -> c4(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(zero(prod(z0, z1)))) A__ADD(s(x0), zero(p(z0))) -> c4(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(zero(p(z0)))) A__ADD(s(x0), zero(add(z0, z1))) -> c4(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(zero(add(z0, z1)))) A__ADD(s(x0), zero(s(z0))) -> c4(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(zero(s(z0)))) A__ADD(s(x0), zero(0)) -> c4(A__ADD(mark(x0), a__zero(0)), MARK(zero(0))) A__ADD(s(x0), zero(true)) -> c4(A__ADD(mark(x0), a__zero(true)), MARK(zero(true))) A__ADD(s(x0), zero(false)) -> c4(A__ADD(mark(x0), a__zero(false)), MARK(zero(false))) A__ADD(s(fact(z0)), zero(x1)) -> c4(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c4(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(zero(z0)), zero(x1)) -> c4(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(p(z0)), zero(x1)) -> c4(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(add(z0, z1)), zero(x1)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(s(z0)), zero(x1)) -> c4(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(0), zero(x1)) -> c4(A__ADD(0, a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(true), zero(x1)) -> c4(A__ADD(true, a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(false), zero(x1)) -> c4(A__ADD(false, a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(x0), zero(x1)) -> c4(MARK(zero(x1))) ---------------------------------------- (220) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1)))) A__ADD(s(x0), prod(x1, x2)) -> c3(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), prod(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, p(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, s(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, 0)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), prod(x1, true)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(x0)) A__ADD(s(x0), prod(x1, false)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(x0)) A__ADD(s(x0), prod(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(p(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(0, x2)) -> c3(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(true, x2)) -> c3(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(false, x2)) -> c3(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), prod(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2)))) A__ADD(s(x0), p(x1)) -> c3(A__ADD(mark(x0), p(mark(x1))), MARK(x0)) A__ADD(s(x0), p(fact(z0))) -> c3(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), p(zero(z0))) -> c3(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(p(z0))) -> c3(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(add(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(s(z0))) -> c3(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(0)) -> c3(A__ADD(mark(x0), a__p(0)), MARK(x0)) A__ADD(s(x0), p(true)) -> c3(A__ADD(mark(x0), a__p(true)), MARK(x0)) A__ADD(s(x0), p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1)))) A__ADD(s(x0), add(x1, x2)) -> c3(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), add(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), add(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, p(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, s(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, 0)) -> c3(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), add(x1, true)) -> c3(A__ADD(mark(x0), a__add(mark(x1), true)), MARK(x0)) A__ADD(s(x0), add(x1, false)) -> c3(A__ADD(mark(x0), a__add(mark(x1), false)), MARK(x0)) A__ADD(s(x0), add(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), add(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(p(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(s(z0), x2)) -> c3(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(0, x2)) -> c3(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) A__ADD(s(x0), add(true, x2)) -> c3(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(x0)) A__ADD(s(x0), add(false, x2)) -> c3(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), add(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), add(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), add(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__add(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), add(x1, x2)) -> c3(A__ADD(0, a__add(mark(x1), mark(x2)))) A__ADD(s(x0), s(fact(z0))) -> c3(A__ADD(mark(x0), s(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), s(zero(z0))) -> c3(A__ADD(mark(x0), s(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(prod(z0, z1))) -> c3(A__ADD(mark(x0), s(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(p(z0))) -> c3(A__ADD(mark(x0), s(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(add(z0, z1))) -> c3(A__ADD(mark(x0), s(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(s(z0))) -> c3(A__ADD(mark(x0), s(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(0)) -> c3(A__ADD(mark(x0), s(0)), MARK(x0)) A__ADD(s(x0), s(true)) -> c3(A__ADD(mark(x0), s(true)), MARK(x0)) A__ADD(s(x0), s(false)) -> c3(A__ADD(mark(x0), s(false)), MARK(x0)) A__ADD(s(fact(z0)), s(x1)) -> c3(A__ADD(a__fact(mark(z0)), s(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), s(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), s(x1)) -> c3(A__ADD(a__zero(mark(z0)), s(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), s(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), s(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), s(x1)) -> c3(A__ADD(a__p(mark(z0)), s(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), s(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), s(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), s(x1)) -> c3(A__ADD(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__ADD(s(0), s(x1)) -> c3(A__ADD(0, s(mark(x1)))) A__ADD(s(fact(z0)), 0) -> c3(A__ADD(a__fact(mark(z0)), 0), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), 0) -> c3(A__ADD(a__if(mark(z0), z1, z2), 0), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), 0) -> c3(A__ADD(a__zero(mark(z0)), 0), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), 0) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), 0), MARK(prod(z0, z1))) A__ADD(s(p(z0)), 0) -> c3(A__ADD(a__p(mark(z0)), 0), MARK(p(z0))) A__ADD(s(add(z0, z1)), 0) -> c3(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) A__ADD(s(s(z0)), 0) -> c3(A__ADD(s(mark(z0)), 0), MARK(s(z0))) A__ADD(s(0), 0) -> c3(A__ADD(0, 0)) A__ADD(s(fact(z0)), true) -> c3(A__ADD(a__fact(mark(z0)), true), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), true) -> c3(A__ADD(a__if(mark(z0), z1, z2), true), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), true) -> c3(A__ADD(a__zero(mark(z0)), true), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), true) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), true), MARK(prod(z0, z1))) A__ADD(s(p(z0)), true) -> c3(A__ADD(a__p(mark(z0)), true), MARK(p(z0))) A__ADD(s(add(z0, z1)), true) -> c3(A__ADD(a__add(mark(z0), mark(z1)), true), MARK(add(z0, z1))) A__ADD(s(s(z0)), true) -> c3(A__ADD(s(mark(z0)), true), MARK(s(z0))) A__ADD(s(0), true) -> c3(A__ADD(0, true)) A__ADD(s(fact(z0)), false) -> c3(A__ADD(a__fact(mark(z0)), false), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), false) -> c3(A__ADD(a__if(mark(z0), z1, z2), false), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), false) -> c3(A__ADD(a__zero(mark(z0)), false), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), false) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), false), MARK(prod(z0, z1))) A__ADD(s(p(z0)), false) -> c3(A__ADD(a__p(mark(z0)), false), MARK(p(z0))) A__ADD(s(add(z0, z1)), false) -> c3(A__ADD(a__add(mark(z0), mark(z1)), false), MARK(add(z0, z1))) A__ADD(s(s(z0)), false) -> c3(A__ADD(s(mark(z0)), false), MARK(s(z0))) A__ADD(s(0), false) -> c3(A__ADD(0, false)) A__ADD(s(fact(x0)), x1) -> c3(A__ADD(a__if(a__zero(mark(mark(x0))), s(0), prod(mark(x0), fact(p(mark(x0))))), mark(x1)), MARK(fact(x0))) A__ADD(s(fact(fact(z0))), x1) -> c3(A__ADD(a__fact(a__fact(mark(z0))), mark(x1)), MARK(fact(fact(z0)))) A__ADD(s(fact(if(z0, z1, z2))), x1) -> c3(A__ADD(a__fact(a__if(mark(z0), z1, z2)), mark(x1)), MARK(fact(if(z0, z1, z2)))) A__ADD(s(fact(zero(z0))), x1) -> c3(A__ADD(a__fact(a__zero(mark(z0))), mark(x1)), MARK(fact(zero(z0)))) A__ADD(s(fact(prod(z0, z1))), x1) -> c3(A__ADD(a__fact(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(fact(prod(z0, z1)))) A__ADD(s(fact(p(z0))), x1) -> c3(A__ADD(a__fact(a__p(mark(z0))), mark(x1)), MARK(fact(p(z0)))) A__ADD(s(fact(add(z0, z1))), x1) -> c3(A__ADD(a__fact(a__add(mark(z0), mark(z1))), mark(x1)), MARK(fact(add(z0, z1)))) A__ADD(s(fact(s(z0))), x1) -> c3(A__ADD(a__fact(s(mark(z0))), mark(x1)), MARK(fact(s(z0)))) A__ADD(s(fact(0)), x1) -> c3(A__ADD(a__fact(0), mark(x1)), MARK(fact(0))) A__ADD(s(fact(true)), x1) -> c3(A__ADD(a__fact(true), 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A__ADD(s(prod(z0, z1)), zero(x1)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(p(z0)), zero(x1)) -> c4(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(add(z0, z1)), zero(x1)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(s(z0)), zero(x1)) -> c4(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(0), zero(x1)) -> c4(A__ADD(0, a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(true), zero(x1)) -> c4(A__ADD(true, a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(false), zero(x1)) -> c4(A__ADD(false, a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(x0), zero(x1)) -> c4(MARK(zero(x1))) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1)))) A__ADD(s(x0), prod(x1, x2)) -> c3(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), prod(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, p(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, s(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, 0)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), prod(x1, true)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(x0)) A__ADD(s(x0), prod(x1, false)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(x0)) A__ADD(s(x0), prod(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(p(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(0, x2)) -> c3(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(true, x2)) -> c3(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(false, x2)) -> c3(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), prod(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2)))) A__ADD(s(x0), p(x1)) -> c3(A__ADD(mark(x0), p(mark(x1))), MARK(x0)) A__ADD(s(x0), p(fact(z0))) -> c3(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), p(zero(z0))) -> c3(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(p(z0))) -> c3(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(add(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(s(z0))) -> c3(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(0)) -> c3(A__ADD(mark(x0), a__p(0)), MARK(x0)) A__ADD(s(x0), p(true)) -> c3(A__ADD(mark(x0), a__p(true)), MARK(x0)) A__ADD(s(x0), p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1)))) A__ADD(s(x0), add(x1, x2)) -> c3(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), add(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), add(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, p(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, s(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, 0)) -> c3(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), add(x1, true)) -> c3(A__ADD(mark(x0), a__add(mark(x1), true)), MARK(x0)) A__ADD(s(x0), add(x1, false)) -> c3(A__ADD(mark(x0), a__add(mark(x1), false)), MARK(x0)) A__ADD(s(x0), add(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), add(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(p(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(s(z0), x2)) -> c3(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(0, x2)) -> c3(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) A__ADD(s(x0), add(true, x2)) -> c3(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(x0)) A__ADD(s(x0), add(false, x2)) -> c3(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), add(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), add(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), add(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__add(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), add(x1, x2)) -> c3(A__ADD(0, a__add(mark(x1), mark(x2)))) A__ADD(s(x0), s(fact(z0))) -> c3(A__ADD(mark(x0), s(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), s(zero(z0))) -> c3(A__ADD(mark(x0), s(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(prod(z0, z1))) -> c3(A__ADD(mark(x0), s(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(p(z0))) -> c3(A__ADD(mark(x0), s(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(add(z0, z1))) -> c3(A__ADD(mark(x0), s(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(s(z0))) -> c3(A__ADD(mark(x0), s(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(0)) -> c3(A__ADD(mark(x0), s(0)), MARK(x0)) A__ADD(s(x0), s(true)) -> c3(A__ADD(mark(x0), s(true)), MARK(x0)) A__ADD(s(x0), s(false)) -> c3(A__ADD(mark(x0), s(false)), MARK(x0)) A__ADD(s(fact(z0)), s(x1)) -> c3(A__ADD(a__fact(mark(z0)), s(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), s(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), s(x1)) -> c3(A__ADD(a__zero(mark(z0)), s(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), s(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), s(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), s(x1)) -> c3(A__ADD(a__p(mark(z0)), s(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), s(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), s(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), s(x1)) -> c3(A__ADD(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__ADD(s(0), s(x1)) -> c3(A__ADD(0, 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A__ADD(s(x0), fact(0)) -> c4(A__ADD(mark(x0), a__fact(0)), MARK(fact(0))) A__ADD(s(x0), fact(true)) -> c4(A__ADD(mark(x0), a__fact(true)), MARK(fact(true))) A__ADD(s(x0), fact(false)) -> c4(A__ADD(mark(x0), a__fact(false)), MARK(fact(false))) A__ADD(s(fact(z0)), fact(x1)) -> c4(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c4(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(zero(z0)), fact(x1)) -> c4(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(p(z0)), fact(x1)) -> c4(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(add(z0, z1)), fact(x1)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(s(z0)), fact(x1)) -> c4(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(0), fact(x1)) -> c4(A__ADD(0, a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(x0), fact(x1)) -> c4(MARK(fact(x1))) A__ADD(s(true), fact(x1)) -> c4(MARK(fact(x1))) A__ADD(s(false), fact(x1)) -> c4(MARK(fact(x1))) A__ADD(s(x0), if(x1, z1, z2)) -> c4(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(if(x1, z1, z2))) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(if(fact(z0), x2, x3))) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(if(if(z0, z1, z2), x2, x3))) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(if(zero(z0), x2, x3))) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(if(prod(z0, z1), x2, x3))) A__ADD(s(x0), if(p(z0), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(if(p(z0), x2, x3))) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(if(add(z0, z1), x2, x3))) A__ADD(s(x0), if(s(z0), x2, x3)) -> c4(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(if(s(z0), x2, x3))) A__ADD(s(x0), if(true, x2, x3)) -> c4(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(if(true, x2, x3))) A__ADD(s(x0), if(false, x2, x3)) -> c4(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(if(false, x2, x3))) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c4(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c4(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c4(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c4(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c4(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(0), if(x1, x2, x3)) -> c4(A__ADD(0, a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(x0), if(0, x2, x3)) -> c4(A__ADD(mark(x0), a__if(0, x2, x3))) A__ADD(s(true), if(x1, x2, x3)) -> c4(MARK(if(x1, x2, x3))) A__ADD(s(false), if(x1, x2, x3)) -> c4(MARK(if(x1, x2, x3))) A__ADD(s(x0), zero(x1)) -> c4(A__ADD(mark(x0), zero(mark(x1))), MARK(zero(x1))) A__ADD(s(x0), zero(fact(z0))) -> c4(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(zero(fact(z0)))) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c4(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(zero(if(z0, z1, z2)))) A__ADD(s(x0), zero(zero(z0))) -> c4(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(zero(zero(z0)))) A__ADD(s(x0), zero(prod(z0, z1))) -> c4(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(zero(prod(z0, z1)))) A__ADD(s(x0), zero(p(z0))) -> c4(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(zero(p(z0)))) A__ADD(s(x0), zero(add(z0, z1))) -> c4(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(zero(add(z0, z1)))) A__ADD(s(x0), zero(s(z0))) -> c4(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(zero(s(z0)))) A__ADD(s(x0), zero(0)) -> c4(A__ADD(mark(x0), a__zero(0)), MARK(zero(0))) A__ADD(s(x0), zero(true)) -> c4(A__ADD(mark(x0), a__zero(true)), MARK(zero(true))) A__ADD(s(x0), zero(false)) -> c4(A__ADD(mark(x0), a__zero(false)), MARK(zero(false))) A__ADD(s(fact(z0)), zero(x1)) -> c4(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c4(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(zero(z0)), zero(x1)) -> c4(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(p(z0)), zero(x1)) -> c4(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(add(z0, z1)), zero(x1)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(s(z0)), zero(x1)) -> c4(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(0), zero(x1)) -> c4(A__ADD(0, a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(true), zero(x1)) -> c4(A__ADD(true, a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(false), zero(x1)) -> c4(A__ADD(false, a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(x0), zero(x1)) -> c4(MARK(zero(x1))) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__PROD_2, A__FACT_1 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c27_1, c21_1, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1, c24_2, c25_2, c25_1, c26_2, c26_1, c_2, c_1, c3_2 ---------------------------------------- (221) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (222) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), 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x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, 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z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2)))) A__ADD(s(x0), p(x1)) -> c3(A__ADD(mark(x0), p(mark(x1))), MARK(x0)) A__ADD(s(x0), p(fact(z0))) -> c3(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), p(zero(z0))) -> c3(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(p(z0))) -> c3(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(add(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(s(z0))) -> c3(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(0)) -> c3(A__ADD(mark(x0), a__p(0)), MARK(x0)) A__ADD(s(x0), p(true)) -> c3(A__ADD(mark(x0), a__p(true)), MARK(x0)) A__ADD(s(x0), p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1)))) A__ADD(s(x0), add(x1, x2)) -> c3(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) 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0)), x2) -> c3(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(add(x0, 0))) A__ADD(s(add(x0, true)), x2) -> c3(A__ADD(a__add(mark(x0), true), mark(x2)), MARK(add(x0, true))) A__ADD(s(add(x0, false)), x2) -> c3(A__ADD(a__add(mark(x0), false), mark(x2)), MARK(add(x0, false))) A__ADD(s(add(fact(z0), x1)), x2) -> c3(A__ADD(a__add(a__fact(mark(z0)), mark(x1)), mark(x2)), MARK(add(fact(z0), x1))) A__ADD(s(add(if(z0, z1, z2), x1)), x2) -> c3(A__ADD(a__add(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(add(if(z0, z1, z2), x1))) A__ADD(s(add(zero(z0), x1)), x2) -> c3(A__ADD(a__add(a__zero(mark(z0)), mark(x1)), mark(x2)), MARK(add(zero(z0), x1))) A__ADD(s(add(prod(z0, z1), x1)), x2) -> c3(A__ADD(a__add(a__prod(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(prod(z0, z1), x1))) A__ADD(s(add(p(z0), x1)), x2) -> c3(A__ADD(a__add(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(add(p(z0), x1))) A__ADD(s(add(add(z0, z1), x1)), x2) -> c3(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(add(z0, z1), x1))) A__ADD(s(add(s(z0), x1)), x2) -> c3(A__ADD(a__add(s(mark(z0)), mark(x1)), mark(x2)), MARK(add(s(z0), x1))) A__ADD(s(add(0, x1)), x2) -> c3(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(add(0, x1))) A__ADD(s(add(true, x1)), x2) -> c3(A__ADD(a__add(true, mark(x1)), mark(x2)), MARK(add(true, x1))) A__ADD(s(add(false, x1)), x2) -> c3(A__ADD(a__add(false, mark(x1)), mark(x2)), MARK(add(false, x1))) A__ADD(s(add(x0, x1)), x2) -> c3(MARK(add(x0, x1))) A__ADD(s(s(fact(z0))), x1) -> c3(A__ADD(s(a__fact(mark(z0))), mark(x1)), MARK(s(fact(z0)))) A__ADD(s(s(if(z0, z1, z2))), x1) -> c3(A__ADD(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(s(if(z0, z1, z2)))) A__ADD(s(s(zero(z0))), x1) -> c3(A__ADD(s(a__zero(mark(z0))), mark(x1)), MARK(s(zero(z0)))) A__ADD(s(s(prod(z0, z1))), x1) -> c3(A__ADD(s(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(s(prod(z0, z1)))) A__ADD(s(s(p(z0))), x1) -> c3(A__ADD(s(a__p(mark(z0))), mark(x1)), MARK(s(p(z0)))) A__ADD(s(s(add(z0, z1))), x1) -> c3(A__ADD(s(a__add(mark(z0), mark(z1))), mark(x1)), MARK(s(add(z0, z1)))) A__ADD(s(s(s(z0))), x1) -> c3(A__ADD(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__ADD(s(s(0)), x1) -> c3(A__ADD(s(0), mark(x1)), MARK(s(0))) A__ADD(s(s(true)), x1) -> c3(A__ADD(s(true), mark(x1)), MARK(s(true))) A__ADD(s(s(false)), x1) -> c3(A__ADD(s(false), mark(x1)), MARK(s(false))) A__ADD(s(s(x0)), x1) -> c3(MARK(s(x0))) A__ADD(s(x0), fact(x1)) -> c4(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(fact(x1))) A__ADD(s(x0), fact(x1)) -> c4(A__ADD(mark(x0), fact(mark(x1))), MARK(fact(x1))) A__ADD(s(x0), fact(fact(z0))) -> c4(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(fact(fact(z0)))) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c4(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(fact(if(z0, z1, z2)))) A__ADD(s(x0), fact(zero(z0))) -> c4(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(fact(zero(z0)))) A__ADD(s(x0), fact(prod(z0, z1))) -> c4(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(fact(prod(z0, z1)))) A__ADD(s(x0), fact(p(z0))) -> c4(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(fact(p(z0)))) A__ADD(s(x0), fact(add(z0, z1))) -> c4(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(fact(add(z0, z1)))) A__ADD(s(x0), fact(s(z0))) -> c4(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(fact(s(z0)))) A__ADD(s(x0), fact(0)) -> c4(A__ADD(mark(x0), a__fact(0)), MARK(fact(0))) A__ADD(s(x0), fact(true)) -> c4(A__ADD(mark(x0), a__fact(true)), MARK(fact(true))) A__ADD(s(x0), fact(false)) -> c4(A__ADD(mark(x0), a__fact(false)), MARK(fact(false))) A__ADD(s(fact(z0)), fact(x1)) -> c4(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c4(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(zero(z0)), fact(x1)) -> c4(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(p(z0)), fact(x1)) -> c4(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(add(z0, z1)), fact(x1)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(s(z0)), fact(x1)) -> c4(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(0), fact(x1)) -> c4(A__ADD(0, a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(x0), fact(x1)) -> c4(MARK(fact(x1))) A__ADD(s(true), fact(x1)) -> c4(MARK(fact(x1))) A__ADD(s(false), fact(x1)) -> c4(MARK(fact(x1))) A__ADD(s(x0), if(x1, z1, z2)) -> c4(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(if(x1, z1, z2))) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(if(fact(z0), x2, x3))) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(if(if(z0, z1, z2), x2, x3))) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(if(zero(z0), x2, x3))) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(if(prod(z0, z1), x2, x3))) A__ADD(s(x0), if(p(z0), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(if(p(z0), x2, x3))) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(if(add(z0, z1), x2, x3))) A__ADD(s(x0), if(s(z0), x2, x3)) -> c4(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(if(s(z0), x2, x3))) A__ADD(s(x0), if(true, x2, x3)) -> c4(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(if(true, x2, x3))) A__ADD(s(x0), if(false, x2, x3)) -> c4(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(if(false, x2, x3))) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c4(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c4(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c4(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c4(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c4(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(0), if(x1, x2, x3)) -> c4(A__ADD(0, a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(x0), if(0, x2, x3)) -> c4(A__ADD(mark(x0), a__if(0, x2, x3))) A__ADD(s(true), if(x1, x2, x3)) -> c4(MARK(if(x1, x2, x3))) A__ADD(s(false), if(x1, x2, x3)) -> c4(MARK(if(x1, x2, x3))) A__ADD(s(x0), zero(x1)) -> c4(A__ADD(mark(x0), zero(mark(x1))), MARK(zero(x1))) A__ADD(s(x0), zero(fact(z0))) -> c4(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(zero(fact(z0)))) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c4(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(zero(if(z0, z1, z2)))) A__ADD(s(x0), zero(zero(z0))) -> c4(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(zero(zero(z0)))) A__ADD(s(x0), zero(prod(z0, z1))) -> c4(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(zero(prod(z0, z1)))) A__ADD(s(x0), zero(p(z0))) -> c4(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(zero(p(z0)))) A__ADD(s(x0), zero(add(z0, z1))) -> c4(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(zero(add(z0, z1)))) A__ADD(s(x0), zero(s(z0))) -> c4(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(zero(s(z0)))) A__ADD(s(x0), zero(0)) -> c4(A__ADD(mark(x0), a__zero(0)), MARK(zero(0))) A__ADD(s(x0), zero(true)) -> c4(A__ADD(mark(x0), a__zero(true)), MARK(zero(true))) A__ADD(s(x0), zero(false)) -> c4(A__ADD(mark(x0), a__zero(false)), MARK(zero(false))) A__ADD(s(fact(z0)), zero(x1)) -> c4(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c4(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(zero(z0)), zero(x1)) -> c4(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(p(z0)), zero(x1)) -> c4(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(add(z0, z1)), zero(x1)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(s(z0)), zero(x1)) -> c4(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(0), zero(x1)) -> c4(A__ADD(0, a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(x0), zero(x1)) -> c4(MARK(zero(x1))) A__ADD(s(true), zero(x1)) -> c4(MARK(zero(x1))) A__ADD(s(false), zero(x1)) -> c4(MARK(zero(x1))) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) 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MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) 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c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), 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c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1)))) A__ADD(s(x0), prod(x1, x2)) -> c3(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), prod(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, p(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, s(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, 0)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), prod(x1, true)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(x0)) A__ADD(s(x0), prod(x1, false)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(x0)) A__ADD(s(x0), prod(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(p(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) 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c3(A__ADD(a__p(mark(z0)), s(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), s(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), s(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), s(x1)) -> c3(A__ADD(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__ADD(s(0), s(x1)) -> c3(A__ADD(0, s(mark(x1)))) A__ADD(s(fact(z0)), 0) -> c3(A__ADD(a__fact(mark(z0)), 0), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), 0) -> c3(A__ADD(a__if(mark(z0), z1, z2), 0), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), 0) -> c3(A__ADD(a__zero(mark(z0)), 0), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), 0) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), 0), MARK(prod(z0, z1))) A__ADD(s(p(z0)), 0) -> c3(A__ADD(a__p(mark(z0)), 0), MARK(p(z0))) A__ADD(s(add(z0, z1)), 0) -> c3(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) A__ADD(s(s(z0)), 0) -> c3(A__ADD(s(mark(z0)), 0), MARK(s(z0))) A__ADD(s(0), 0) -> c3(A__ADD(0, 0)) A__ADD(s(fact(z0)), true) -> c3(A__ADD(a__fact(mark(z0)), true), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), true) -> c3(A__ADD(a__if(mark(z0), z1, z2), true), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), true) -> c3(A__ADD(a__zero(mark(z0)), true), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), true) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), true), MARK(prod(z0, z1))) A__ADD(s(p(z0)), true) -> c3(A__ADD(a__p(mark(z0)), true), MARK(p(z0))) A__ADD(s(add(z0, z1)), true) -> c3(A__ADD(a__add(mark(z0), mark(z1)), true), MARK(add(z0, z1))) A__ADD(s(s(z0)), true) -> c3(A__ADD(s(mark(z0)), true), MARK(s(z0))) A__ADD(s(0), true) -> c3(A__ADD(0, true)) A__ADD(s(fact(z0)), false) -> c3(A__ADD(a__fact(mark(z0)), false), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), false) -> c3(A__ADD(a__if(mark(z0), z1, z2), false), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), false) -> c3(A__ADD(a__zero(mark(z0)), false), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), false) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), false), MARK(prod(z0, z1))) A__ADD(s(p(z0)), false) -> c3(A__ADD(a__p(mark(z0)), false), MARK(p(z0))) A__ADD(s(add(z0, z1)), false) -> c3(A__ADD(a__add(mark(z0), mark(z1)), false), MARK(add(z0, z1))) A__ADD(s(s(z0)), false) -> c3(A__ADD(s(mark(z0)), false), MARK(s(z0))) A__ADD(s(0), false) -> c3(A__ADD(0, false)) A__ADD(s(fact(x0)), x1) -> c3(A__ADD(a__if(a__zero(mark(mark(x0))), s(0), prod(mark(x0), fact(p(mark(x0))))), mark(x1)), MARK(fact(x0))) A__ADD(s(fact(fact(z0))), x1) -> c3(A__ADD(a__fact(a__fact(mark(z0))), mark(x1)), MARK(fact(fact(z0)))) A__ADD(s(fact(if(z0, z1, z2))), x1) -> c3(A__ADD(a__fact(a__if(mark(z0), z1, z2)), mark(x1)), MARK(fact(if(z0, z1, z2)))) A__ADD(s(fact(zero(z0))), x1) -> c3(A__ADD(a__fact(a__zero(mark(z0))), mark(x1)), MARK(fact(zero(z0)))) A__ADD(s(fact(prod(z0, z1))), x1) -> c3(A__ADD(a__fact(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(fact(prod(z0, z1)))) A__ADD(s(fact(p(z0))), x1) -> c3(A__ADD(a__fact(a__p(mark(z0))), mark(x1)), MARK(fact(p(z0)))) A__ADD(s(fact(add(z0, z1))), x1) -> c3(A__ADD(a__fact(a__add(mark(z0), mark(z1))), mark(x1)), MARK(fact(add(z0, z1)))) 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c3(A__ADD(a__zero(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(zero(prod(z0, z1)))) A__ADD(s(zero(p(z0))), x1) -> c3(A__ADD(a__zero(a__p(mark(z0))), mark(x1)), MARK(zero(p(z0)))) A__ADD(s(zero(add(z0, z1))), x1) -> c3(A__ADD(a__zero(a__add(mark(z0), mark(z1))), mark(x1)), MARK(zero(add(z0, z1)))) A__ADD(s(zero(s(z0))), x1) -> c3(A__ADD(a__zero(s(mark(z0))), mark(x1)), MARK(zero(s(z0)))) A__ADD(s(zero(0)), x1) -> c3(A__ADD(a__zero(0), mark(x1)), MARK(zero(0))) A__ADD(s(zero(true)), x1) -> c3(A__ADD(a__zero(true), mark(x1)), MARK(zero(true))) A__ADD(s(zero(false)), x1) -> c3(A__ADD(a__zero(false), mark(x1)), MARK(zero(false))) A__ADD(s(zero(x0)), x1) -> c3(MARK(zero(x0))) A__ADD(s(prod(x0, fact(z0))), x2) -> c3(A__ADD(a__prod(mark(x0), a__fact(mark(z0))), mark(x2)), MARK(prod(x0, fact(z0)))) A__ADD(s(prod(x0, if(z0, z1, z2))), x2) -> c3(A__ADD(a__prod(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(prod(x0, if(z0, z1, z2)))) A__ADD(s(prod(x0, zero(z0))), x2) -> c3(A__ADD(a__prod(mark(x0), a__zero(mark(z0))), mark(x2)), MARK(prod(x0, zero(z0)))) A__ADD(s(prod(x0, prod(z0, z1))), x2) -> c3(A__ADD(a__prod(mark(x0), a__prod(mark(z0), mark(z1))), mark(x2)), MARK(prod(x0, prod(z0, z1)))) A__ADD(s(prod(x0, p(z0))), x2) -> c3(A__ADD(a__prod(mark(x0), a__p(mark(z0))), mark(x2)), MARK(prod(x0, p(z0)))) A__ADD(s(prod(x0, add(z0, z1))), x2) -> c3(A__ADD(a__prod(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(prod(x0, add(z0, z1)))) A__ADD(s(prod(x0, s(z0))), x2) -> c3(A__ADD(a__prod(mark(x0), s(mark(z0))), mark(x2)), MARK(prod(x0, s(z0)))) A__ADD(s(prod(x0, 0)), x2) -> c3(A__ADD(a__prod(mark(x0), 0), mark(x2)), MARK(prod(x0, 0))) A__ADD(s(prod(x0, true)), x2) -> c3(A__ADD(a__prod(mark(x0), true), mark(x2)), MARK(prod(x0, true))) A__ADD(s(prod(x0, false)), x2) -> c3(A__ADD(a__prod(mark(x0), false), mark(x2)), MARK(prod(x0, false))) A__ADD(s(prod(fact(z0), x1)), x2) -> c3(A__ADD(a__prod(a__fact(mark(z0)), mark(x1)), mark(x2)), MARK(prod(fact(z0), x1))) A__ADD(s(prod(if(z0, z1, z2), x1)), x2) -> c3(A__ADD(a__prod(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(prod(if(z0, z1, z2), x1))) A__ADD(s(prod(zero(z0), x1)), x2) -> c3(A__ADD(a__prod(a__zero(mark(z0)), mark(x1)), mark(x2)), MARK(prod(zero(z0), x1))) A__ADD(s(prod(prod(z0, z1), x1)), x2) -> c3(A__ADD(a__prod(a__prod(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(prod(prod(z0, z1), x1))) A__ADD(s(prod(p(z0), x1)), x2) -> c3(A__ADD(a__prod(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(prod(p(z0), x1))) A__ADD(s(prod(add(z0, z1), x1)), x2) -> c3(A__ADD(a__prod(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(prod(add(z0, z1), x1))) A__ADD(s(prod(s(z0), x1)), x2) -> c3(A__ADD(a__prod(s(mark(z0)), mark(x1)), mark(x2)), MARK(prod(s(z0), x1))) A__ADD(s(prod(0, x1)), x2) -> c3(A__ADD(a__prod(0, mark(x1)), mark(x2)), MARK(prod(0, x1))) A__ADD(s(prod(true, x1)), x2) -> c3(A__ADD(a__prod(true, mark(x1)), mark(x2)), MARK(prod(true, x1))) A__ADD(s(prod(false, x1)), x2) -> c3(A__ADD(a__prod(false, mark(x1)), mark(x2)), MARK(prod(false, x1))) A__ADD(s(prod(x0, x1)), x2) -> c3(MARK(prod(x0, x1))) A__ADD(s(p(fact(z0))), x1) -> c3(A__ADD(a__p(a__fact(mark(z0))), mark(x1)), MARK(p(fact(z0)))) A__ADD(s(p(if(z0, z1, z2))), x1) -> c3(A__ADD(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2)))) A__ADD(s(p(zero(z0))), x1) -> c3(A__ADD(a__p(a__zero(mark(z0))), mark(x1)), MARK(p(zero(z0)))) A__ADD(s(p(prod(z0, z1))), x1) -> c3(A__ADD(a__p(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(p(prod(z0, z1)))) A__ADD(s(p(p(z0))), x1) -> c3(A__ADD(a__p(a__p(mark(z0))), mark(x1)), MARK(p(p(z0)))) A__ADD(s(p(add(z0, z1))), x1) -> c3(A__ADD(a__p(a__add(mark(z0), mark(z1))), mark(x1)), MARK(p(add(z0, z1)))) A__ADD(s(p(s(z0))), x1) -> c3(A__ADD(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0)))) A__ADD(s(p(x0)), x1) -> c3(MARK(p(x0))) A__ADD(s(p(0)), x1) -> c3(A__ADD(a__p(0), mark(x1))) A__ADD(s(p(true)), x1) -> c3(A__ADD(a__p(true), mark(x1))) A__ADD(s(p(false)), x1) -> c3(A__ADD(a__p(false), mark(x1))) A__ADD(s(add(x0, fact(z0))), x2) -> c3(A__ADD(a__add(mark(x0), a__fact(mark(z0))), mark(x2)), MARK(add(x0, fact(z0)))) A__ADD(s(add(x0, if(z0, z1, z2))), x2) -> c3(A__ADD(a__add(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(add(x0, if(z0, z1, z2)))) A__ADD(s(add(x0, zero(z0))), x2) -> c3(A__ADD(a__add(mark(x0), a__zero(mark(z0))), mark(x2)), MARK(add(x0, zero(z0)))) A__ADD(s(add(x0, prod(z0, z1))), x2) -> c3(A__ADD(a__add(mark(x0), a__prod(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, prod(z0, z1)))) A__ADD(s(add(x0, p(z0))), x2) -> c3(A__ADD(a__add(mark(x0), a__p(mark(z0))), mark(x2)), MARK(add(x0, p(z0)))) A__ADD(s(add(x0, add(z0, z1))), x2) -> c3(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, add(z0, z1)))) A__ADD(s(add(x0, s(z0))), x2) -> c3(A__ADD(a__add(mark(x0), s(mark(z0))), mark(x2)), MARK(add(x0, s(z0)))) A__ADD(s(add(x0, 0)), x2) -> c3(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(add(x0, 0))) A__ADD(s(add(x0, true)), x2) -> c3(A__ADD(a__add(mark(x0), true), mark(x2)), MARK(add(x0, true))) A__ADD(s(add(x0, false)), x2) -> c3(A__ADD(a__add(mark(x0), false), mark(x2)), MARK(add(x0, false))) A__ADD(s(add(fact(z0), x1)), x2) -> c3(A__ADD(a__add(a__fact(mark(z0)), mark(x1)), mark(x2)), MARK(add(fact(z0), x1))) A__ADD(s(add(if(z0, z1, z2), x1)), x2) -> c3(A__ADD(a__add(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(add(if(z0, z1, z2), x1))) A__ADD(s(add(zero(z0), x1)), x2) -> c3(A__ADD(a__add(a__zero(mark(z0)), mark(x1)), mark(x2)), MARK(add(zero(z0), x1))) A__ADD(s(add(prod(z0, z1), x1)), x2) -> c3(A__ADD(a__add(a__prod(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(prod(z0, z1), x1))) A__ADD(s(add(p(z0), x1)), x2) -> c3(A__ADD(a__add(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(add(p(z0), x1))) A__ADD(s(add(add(z0, z1), x1)), x2) -> c3(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(add(z0, z1), x1))) A__ADD(s(add(s(z0), x1)), x2) -> c3(A__ADD(a__add(s(mark(z0)), mark(x1)), mark(x2)), MARK(add(s(z0), x1))) A__ADD(s(add(0, x1)), x2) -> c3(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(add(0, x1))) A__ADD(s(add(true, x1)), x2) -> c3(A__ADD(a__add(true, mark(x1)), mark(x2)), MARK(add(true, x1))) A__ADD(s(add(false, x1)), x2) -> c3(A__ADD(a__add(false, mark(x1)), mark(x2)), MARK(add(false, x1))) A__ADD(s(add(x0, x1)), x2) -> c3(MARK(add(x0, x1))) A__ADD(s(s(fact(z0))), x1) -> c3(A__ADD(s(a__fact(mark(z0))), mark(x1)), MARK(s(fact(z0)))) A__ADD(s(s(if(z0, z1, z2))), x1) -> c3(A__ADD(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(s(if(z0, z1, z2)))) A__ADD(s(s(zero(z0))), x1) -> c3(A__ADD(s(a__zero(mark(z0))), mark(x1)), MARK(s(zero(z0)))) A__ADD(s(s(prod(z0, z1))), x1) -> c3(A__ADD(s(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(s(prod(z0, z1)))) A__ADD(s(s(p(z0))), x1) -> c3(A__ADD(s(a__p(mark(z0))), mark(x1)), MARK(s(p(z0)))) A__ADD(s(s(add(z0, z1))), x1) -> c3(A__ADD(s(a__add(mark(z0), mark(z1))), mark(x1)), MARK(s(add(z0, z1)))) A__ADD(s(s(s(z0))), x1) -> c3(A__ADD(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__ADD(s(s(0)), x1) -> c3(A__ADD(s(0), mark(x1)), MARK(s(0))) A__ADD(s(s(true)), x1) -> c3(A__ADD(s(true), mark(x1)), MARK(s(true))) A__ADD(s(s(false)), x1) -> c3(A__ADD(s(false), mark(x1)), MARK(s(false))) A__ADD(s(s(x0)), x1) -> c3(MARK(s(x0))) A__ADD(s(x0), fact(x1)) -> c4(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(fact(x1))) A__ADD(s(x0), fact(x1)) -> c4(A__ADD(mark(x0), fact(mark(x1))), MARK(fact(x1))) A__ADD(s(x0), fact(fact(z0))) -> c4(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(fact(fact(z0)))) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c4(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(fact(if(z0, z1, z2)))) A__ADD(s(x0), fact(zero(z0))) -> c4(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(fact(zero(z0)))) A__ADD(s(x0), fact(prod(z0, z1))) -> c4(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(fact(prod(z0, z1)))) A__ADD(s(x0), fact(p(z0))) -> c4(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(fact(p(z0)))) A__ADD(s(x0), fact(add(z0, z1))) -> c4(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(fact(add(z0, z1)))) A__ADD(s(x0), fact(s(z0))) -> c4(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(fact(s(z0)))) A__ADD(s(x0), fact(0)) -> c4(A__ADD(mark(x0), a__fact(0)), MARK(fact(0))) A__ADD(s(x0), fact(true)) -> c4(A__ADD(mark(x0), a__fact(true)), MARK(fact(true))) A__ADD(s(x0), fact(false)) -> c4(A__ADD(mark(x0), a__fact(false)), MARK(fact(false))) A__ADD(s(fact(z0)), fact(x1)) -> c4(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c4(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(zero(z0)), fact(x1)) -> c4(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(p(z0)), fact(x1)) -> c4(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(add(z0, z1)), fact(x1)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(s(z0)), fact(x1)) -> c4(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(0), fact(x1)) -> c4(A__ADD(0, a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(x0), fact(x1)) -> c4(MARK(fact(x1))) A__ADD(s(true), fact(x1)) -> c4(MARK(fact(x1))) A__ADD(s(false), fact(x1)) -> c4(MARK(fact(x1))) A__ADD(s(x0), if(x1, z1, z2)) -> c4(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(if(x1, z1, z2))) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(if(fact(z0), x2, x3))) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(if(if(z0, z1, z2), x2, x3))) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(if(zero(z0), x2, x3))) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(if(prod(z0, z1), x2, x3))) A__ADD(s(x0), if(p(z0), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(if(p(z0), x2, x3))) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(if(add(z0, z1), x2, x3))) A__ADD(s(x0), if(s(z0), x2, x3)) -> c4(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(if(s(z0), x2, x3))) A__ADD(s(x0), if(true, x2, x3)) -> c4(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(if(true, x2, x3))) A__ADD(s(x0), if(false, x2, x3)) -> c4(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(if(false, x2, x3))) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c4(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c4(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c4(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c4(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c4(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(0), if(x1, x2, x3)) -> c4(A__ADD(0, a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(x0), if(0, x2, x3)) -> c4(A__ADD(mark(x0), a__if(0, x2, x3))) A__ADD(s(true), if(x1, x2, x3)) -> c4(MARK(if(x1, x2, x3))) A__ADD(s(false), if(x1, x2, x3)) -> c4(MARK(if(x1, x2, x3))) A__ADD(s(x0), zero(x1)) -> c4(A__ADD(mark(x0), zero(mark(x1))), MARK(zero(x1))) A__ADD(s(x0), zero(fact(z0))) -> c4(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(zero(fact(z0)))) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c4(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(zero(if(z0, z1, z2)))) A__ADD(s(x0), zero(zero(z0))) -> c4(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(zero(zero(z0)))) A__ADD(s(x0), zero(prod(z0, z1))) -> c4(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(zero(prod(z0, z1)))) A__ADD(s(x0), zero(p(z0))) -> c4(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(zero(p(z0)))) A__ADD(s(x0), zero(add(z0, z1))) -> c4(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(zero(add(z0, z1)))) A__ADD(s(x0), zero(s(z0))) -> c4(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(zero(s(z0)))) A__ADD(s(x0), zero(0)) -> c4(A__ADD(mark(x0), a__zero(0)), MARK(zero(0))) A__ADD(s(x0), zero(true)) -> c4(A__ADD(mark(x0), a__zero(true)), MARK(zero(true))) A__ADD(s(x0), zero(false)) -> c4(A__ADD(mark(x0), a__zero(false)), MARK(zero(false))) A__ADD(s(fact(z0)), zero(x1)) -> c4(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c4(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(zero(z0)), zero(x1)) -> c4(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(p(z0)), zero(x1)) -> c4(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(add(z0, z1)), zero(x1)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(s(z0)), zero(x1)) -> c4(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(0), zero(x1)) -> c4(A__ADD(0, a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(x0), zero(x1)) -> c4(MARK(zero(x1))) A__ADD(s(true), zero(x1)) -> c4(MARK(zero(x1))) A__ADD(s(false), zero(x1)) -> c4(MARK(zero(x1))) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__PROD_2, A__FACT_1 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c27_1, c21_1, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1, c24_2, c25_2, c25_1, c26_2, c26_1, c_2, c_1, c3_2 ---------------------------------------- (223) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__ADD(s(x0), prod(z0, z1)) -> c4(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) by A__ADD(s(x0), prod(x1, x2)) -> c4(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(x0), prod(x1, fact(z0))) -> c4(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(prod(x1, fact(z0)))) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c4(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(prod(x1, if(z0, z1, z2)))) A__ADD(s(x0), prod(x1, zero(z0))) -> c4(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(prod(x1, zero(z0)))) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c4(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(prod(x1, prod(z0, z1)))) A__ADD(s(x0), prod(x1, p(z0))) -> c4(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(prod(x1, p(z0)))) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c4(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(prod(x1, add(z0, z1)))) A__ADD(s(x0), prod(x1, s(z0))) -> c4(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(prod(x1, s(z0)))) A__ADD(s(x0), prod(x1, 0)) -> c4(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(prod(x1, 0))) A__ADD(s(x0), prod(x1, true)) -> c4(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(prod(x1, true))) A__ADD(s(x0), prod(x1, false)) -> c4(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(prod(x1, false))) A__ADD(s(x0), prod(fact(z0), x2)) -> c4(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(prod(fact(z0), x2))) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c4(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(prod(if(z0, z1, z2), x2))) A__ADD(s(x0), prod(zero(z0), x2)) -> c4(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(prod(zero(z0), x2))) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c4(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(prod(prod(z0, z1), x2))) A__ADD(s(x0), prod(p(z0), x2)) -> c4(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(prod(p(z0), x2))) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c4(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(prod(add(z0, z1), x2))) A__ADD(s(x0), prod(s(z0), x2)) -> c4(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(prod(s(z0), x2))) A__ADD(s(x0), prod(0, x2)) -> c4(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(prod(0, x2))) A__ADD(s(x0), prod(true, x2)) -> c4(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(prod(true, x2))) A__ADD(s(x0), prod(false, x2)) -> c4(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(prod(false, x2))) A__ADD(s(fact(z0)), prod(x1, x2)) -> c4(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c4(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c4(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(p(z0)), prod(x1, x2)) -> c4(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(s(z0)), prod(x1, x2)) -> c4(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(0), prod(x1, x2)) -> c4(A__ADD(0, a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(true), prod(x1, x2)) -> c4(A__ADD(true, a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(false), prod(x1, x2)) -> c4(A__ADD(false, a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) ---------------------------------------- (224) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1)))) A__ADD(s(x0), prod(x1, x2)) -> c3(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), prod(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, p(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, s(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, 0)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), prod(x1, true)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(x0)) A__ADD(s(x0), prod(x1, false)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(x0)) A__ADD(s(x0), prod(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(p(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(0, x2)) -> c3(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(true, x2)) -> c3(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(false, x2)) -> c3(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), prod(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2)))) A__ADD(s(x0), p(x1)) -> c3(A__ADD(mark(x0), p(mark(x1))), MARK(x0)) A__ADD(s(x0), p(fact(z0))) -> c3(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), p(zero(z0))) -> c3(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(p(z0))) -> c3(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(add(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(s(z0))) -> c3(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(0)) -> c3(A__ADD(mark(x0), a__p(0)), MARK(x0)) A__ADD(s(x0), p(true)) -> c3(A__ADD(mark(x0), a__p(true)), MARK(x0)) A__ADD(s(x0), p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1)))) A__ADD(s(x0), add(x1, x2)) -> c3(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), add(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), add(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, p(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, s(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, 0)) -> c3(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), add(x1, true)) -> c3(A__ADD(mark(x0), a__add(mark(x1), true)), MARK(x0)) A__ADD(s(x0), add(x1, false)) -> c3(A__ADD(mark(x0), a__add(mark(x1), false)), MARK(x0)) A__ADD(s(x0), add(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), 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x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(if(p(z0), x2, x3))) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(if(add(z0, z1), x2, x3))) A__ADD(s(x0), if(s(z0), x2, x3)) -> c4(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(if(s(z0), x2, x3))) A__ADD(s(x0), if(true, x2, x3)) -> c4(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(if(true, x2, x3))) A__ADD(s(x0), if(false, x2, x3)) -> c4(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(if(false, x2, x3))) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c4(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c4(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c4(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c4(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c4(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(0), if(x1, x2, x3)) -> c4(A__ADD(0, a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(x0), if(0, x2, x3)) -> c4(A__ADD(mark(x0), a__if(0, x2, x3))) A__ADD(s(true), if(x1, x2, x3)) -> c4(MARK(if(x1, x2, x3))) A__ADD(s(false), if(x1, x2, x3)) -> c4(MARK(if(x1, x2, x3))) A__ADD(s(x0), zero(x1)) -> c4(A__ADD(mark(x0), zero(mark(x1))), MARK(zero(x1))) A__ADD(s(x0), zero(fact(z0))) -> c4(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(zero(fact(z0)))) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c4(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(zero(if(z0, z1, z2)))) A__ADD(s(x0), zero(zero(z0))) -> c4(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(zero(zero(z0)))) A__ADD(s(x0), zero(prod(z0, z1))) -> c4(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(zero(prod(z0, z1)))) A__ADD(s(x0), zero(p(z0))) -> c4(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(zero(p(z0)))) A__ADD(s(x0), zero(add(z0, z1))) -> c4(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(zero(add(z0, z1)))) A__ADD(s(x0), zero(s(z0))) -> c4(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(zero(s(z0)))) A__ADD(s(x0), zero(0)) -> c4(A__ADD(mark(x0), a__zero(0)), MARK(zero(0))) A__ADD(s(x0), zero(true)) -> c4(A__ADD(mark(x0), a__zero(true)), MARK(zero(true))) A__ADD(s(x0), zero(false)) -> c4(A__ADD(mark(x0), a__zero(false)), MARK(zero(false))) A__ADD(s(fact(z0)), zero(x1)) -> c4(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c4(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(zero(z0)), zero(x1)) -> c4(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(p(z0)), zero(x1)) -> c4(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(add(z0, z1)), zero(x1)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(s(z0)), zero(x1)) -> c4(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(0), zero(x1)) -> c4(A__ADD(0, a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(x0), zero(x1)) -> c4(MARK(zero(x1))) A__ADD(s(true), zero(x1)) -> c4(MARK(zero(x1))) A__ADD(s(false), zero(x1)) -> c4(MARK(zero(x1))) A__ADD(s(x0), prod(x1, x2)) -> c4(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(x0), prod(x1, fact(z0))) -> c4(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(prod(x1, fact(z0)))) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c4(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(prod(x1, if(z0, z1, z2)))) A__ADD(s(x0), prod(x1, zero(z0))) -> c4(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(prod(x1, zero(z0)))) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c4(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(prod(x1, prod(z0, z1)))) A__ADD(s(x0), prod(x1, p(z0))) -> c4(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(prod(x1, p(z0)))) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c4(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(prod(x1, add(z0, z1)))) A__ADD(s(x0), prod(x1, s(z0))) -> c4(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(prod(x1, s(z0)))) A__ADD(s(x0), prod(x1, 0)) -> c4(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(prod(x1, 0))) A__ADD(s(x0), prod(x1, true)) -> c4(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(prod(x1, true))) A__ADD(s(x0), prod(x1, false)) -> c4(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(prod(x1, false))) A__ADD(s(x0), 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c4(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(prod(true, x2))) A__ADD(s(x0), prod(false, x2)) -> c4(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(prod(false, x2))) A__ADD(s(fact(z0)), prod(x1, x2)) -> c4(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c4(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c4(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(p(z0)), prod(x1, x2)) -> c4(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(s(z0)), prod(x1, x2)) -> c4(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(0), prod(x1, x2)) -> c4(A__ADD(0, a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(true), prod(x1, x2)) -> c4(A__ADD(true, a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(false), prod(x1, x2)) -> c4(A__ADD(false, a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), 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MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) 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z2), x2, x3)), MARK(if(if(z0, z1, z2), x2, x3))) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(if(zero(z0), x2, x3))) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(if(prod(z0, z1), x2, x3))) A__ADD(s(x0), if(p(z0), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(if(p(z0), x2, x3))) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(if(add(z0, z1), x2, x3))) A__ADD(s(x0), if(s(z0), x2, x3)) -> c4(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(if(s(z0), x2, x3))) A__ADD(s(x0), if(true, x2, x3)) -> c4(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(if(true, x2, x3))) A__ADD(s(x0), if(false, x2, x3)) -> c4(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(if(false, x2, x3))) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c4(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c4(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c4(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c4(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c4(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(0), if(x1, x2, x3)) -> c4(A__ADD(0, a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(x0), if(0, x2, x3)) -> c4(A__ADD(mark(x0), a__if(0, x2, x3))) A__ADD(s(true), if(x1, x2, x3)) -> c4(MARK(if(x1, x2, x3))) A__ADD(s(false), if(x1, x2, x3)) -> c4(MARK(if(x1, x2, x3))) A__ADD(s(x0), zero(x1)) -> c4(A__ADD(mark(x0), zero(mark(x1))), MARK(zero(x1))) A__ADD(s(x0), zero(fact(z0))) -> c4(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(zero(fact(z0)))) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c4(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(zero(if(z0, z1, z2)))) A__ADD(s(x0), zero(zero(z0))) -> c4(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(zero(zero(z0)))) A__ADD(s(x0), zero(prod(z0, z1))) -> c4(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(zero(prod(z0, z1)))) A__ADD(s(x0), zero(p(z0))) -> c4(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(zero(p(z0)))) A__ADD(s(x0), zero(add(z0, z1))) -> c4(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(zero(add(z0, z1)))) A__ADD(s(x0), zero(s(z0))) -> c4(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(zero(s(z0)))) A__ADD(s(x0), zero(0)) -> c4(A__ADD(mark(x0), a__zero(0)), MARK(zero(0))) A__ADD(s(x0), zero(true)) -> c4(A__ADD(mark(x0), a__zero(true)), MARK(zero(true))) A__ADD(s(x0), zero(false)) -> c4(A__ADD(mark(x0), a__zero(false)), MARK(zero(false))) A__ADD(s(fact(z0)), zero(x1)) -> c4(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c4(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(zero(z0)), zero(x1)) -> c4(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(p(z0)), zero(x1)) -> c4(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(add(z0, z1)), zero(x1)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(s(z0)), zero(x1)) -> c4(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(0), zero(x1)) -> c4(A__ADD(0, a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(x0), zero(x1)) -> c4(MARK(zero(x1))) A__ADD(s(true), zero(x1)) -> c4(MARK(zero(x1))) A__ADD(s(false), zero(x1)) -> c4(MARK(zero(x1))) A__ADD(s(x0), prod(x1, x2)) -> c4(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(x0), prod(x1, fact(z0))) -> c4(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(prod(x1, fact(z0)))) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c4(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(prod(x1, if(z0, z1, z2)))) A__ADD(s(x0), prod(x1, zero(z0))) -> c4(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(prod(x1, zero(z0)))) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c4(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(prod(x1, prod(z0, z1)))) A__ADD(s(x0), prod(x1, p(z0))) -> c4(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(prod(x1, p(z0)))) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c4(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(prod(x1, add(z0, z1)))) A__ADD(s(x0), prod(x1, s(z0))) -> c4(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(prod(x1, s(z0)))) A__ADD(s(x0), prod(x1, 0)) -> c4(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(prod(x1, 0))) A__ADD(s(x0), prod(x1, true)) -> c4(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(prod(x1, true))) A__ADD(s(x0), prod(x1, false)) -> c4(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(prod(x1, false))) A__ADD(s(x0), prod(fact(z0), x2)) -> c4(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(prod(fact(z0), x2))) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c4(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(prod(if(z0, z1, z2), x2))) A__ADD(s(x0), prod(zero(z0), x2)) -> c4(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(prod(zero(z0), x2))) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c4(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(prod(prod(z0, z1), x2))) A__ADD(s(x0), prod(p(z0), x2)) -> c4(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(prod(p(z0), x2))) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c4(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(prod(add(z0, z1), x2))) A__ADD(s(x0), prod(s(z0), x2)) -> c4(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(prod(s(z0), x2))) A__ADD(s(x0), prod(0, x2)) -> c4(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(prod(0, x2))) A__ADD(s(x0), prod(true, x2)) -> c4(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(prod(true, x2))) A__ADD(s(x0), prod(false, x2)) -> c4(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(prod(false, x2))) A__ADD(s(fact(z0)), prod(x1, x2)) -> c4(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c4(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c4(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(p(z0)), prod(x1, x2)) -> c4(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(s(z0)), prod(x1, x2)) -> c4(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(0), prod(x1, x2)) -> c4(A__ADD(0, a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(true), prod(x1, x2)) -> c4(A__ADD(true, a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(false), prod(x1, x2)) -> c4(A__ADD(false, a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__PROD_2, A__FACT_1 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c27_1, c21_1, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1, c24_2, c25_2, c25_1, c26_2, c26_1, c_2, c_1, c3_2 ---------------------------------------- (225) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (226) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> 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true))) A__ADD(s(x0), prod(x1, false)) -> c4(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(prod(x1, false))) A__ADD(s(x0), prod(fact(z0), x2)) -> c4(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(prod(fact(z0), x2))) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c4(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(prod(if(z0, z1, z2), x2))) A__ADD(s(x0), prod(zero(z0), x2)) -> c4(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(prod(zero(z0), x2))) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c4(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(prod(prod(z0, z1), x2))) A__ADD(s(x0), prod(p(z0), x2)) -> c4(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(prod(p(z0), x2))) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c4(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(prod(add(z0, z1), x2))) A__ADD(s(x0), prod(s(z0), x2)) -> c4(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(prod(s(z0), x2))) A__ADD(s(x0), prod(0, x2)) -> c4(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(prod(0, x2))) A__ADD(s(x0), prod(true, x2)) -> c4(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(prod(true, x2))) A__ADD(s(x0), prod(false, x2)) -> c4(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(prod(false, x2))) A__ADD(s(fact(z0)), prod(x1, x2)) -> c4(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c4(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c4(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(p(z0)), prod(x1, x2)) -> c4(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(s(z0)), prod(x1, x2)) -> c4(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(0), prod(x1, x2)) -> c4(A__ADD(0, a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(true), prod(x1, x2)) -> c4(MARK(prod(x1, x2))) A__ADD(s(false), prod(x1, x2)) -> c4(MARK(prod(x1, x2))) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) 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c3(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(s(z0))) -> c3(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(0)) -> c3(A__ADD(mark(x0), a__p(0)), MARK(x0)) A__ADD(s(x0), p(true)) -> c3(A__ADD(mark(x0), a__p(true)), MARK(x0)) A__ADD(s(x0), p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1)))) A__ADD(s(x0), add(x1, x2)) -> c3(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), add(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), add(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, p(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, s(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, 0)) -> c3(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), add(x1, true)) -> c3(A__ADD(mark(x0), a__add(mark(x1), true)), MARK(x0)) A__ADD(s(x0), add(x1, false)) -> c3(A__ADD(mark(x0), a__add(mark(x1), false)), MARK(x0)) A__ADD(s(x0), add(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), add(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(p(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(s(z0), x2)) -> c3(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(0, x2)) -> c3(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) A__ADD(s(x0), add(true, x2)) -> c3(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(x0)) A__ADD(s(x0), add(false, x2)) -> c3(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), add(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), add(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), add(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__add(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), add(x1, x2)) -> c3(A__ADD(0, a__add(mark(x1), mark(x2)))) A__ADD(s(x0), s(fact(z0))) -> c3(A__ADD(mark(x0), s(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), s(zero(z0))) -> c3(A__ADD(mark(x0), s(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(prod(z0, z1))) -> c3(A__ADD(mark(x0), s(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(p(z0))) -> c3(A__ADD(mark(x0), s(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(add(z0, z1))) -> c3(A__ADD(mark(x0), s(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(s(z0))) -> c3(A__ADD(mark(x0), s(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(0)) -> c3(A__ADD(mark(x0), s(0)), MARK(x0)) A__ADD(s(x0), s(true)) -> c3(A__ADD(mark(x0), s(true)), MARK(x0)) A__ADD(s(x0), s(false)) -> c3(A__ADD(mark(x0), s(false)), MARK(x0)) A__ADD(s(fact(z0)), s(x1)) -> c3(A__ADD(a__fact(mark(z0)), s(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), s(x1)) -> 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c3(A__ADD(a__fact(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(fact(prod(z0, z1)))) A__ADD(s(fact(p(z0))), x1) -> c3(A__ADD(a__fact(a__p(mark(z0))), mark(x1)), MARK(fact(p(z0)))) A__ADD(s(fact(add(z0, z1))), x1) -> c3(A__ADD(a__fact(a__add(mark(z0), mark(z1))), mark(x1)), MARK(fact(add(z0, z1)))) A__ADD(s(fact(s(z0))), x1) -> c3(A__ADD(a__fact(s(mark(z0))), mark(x1)), MARK(fact(s(z0)))) A__ADD(s(fact(0)), x1) -> c3(A__ADD(a__fact(0), mark(x1)), MARK(fact(0))) A__ADD(s(fact(true)), x1) -> c3(A__ADD(a__fact(true), mark(x1)), MARK(fact(true))) A__ADD(s(fact(false)), x1) -> c3(A__ADD(a__fact(false), mark(x1)), MARK(fact(false))) A__ADD(s(fact(x0)), x1) -> c3(MARK(fact(x0))) A__ADD(s(if(fact(z0), x1, x2)), x3) -> c3(A__ADD(a__if(a__fact(mark(z0)), x1, x2), mark(x3)), MARK(if(fact(z0), x1, x2))) A__ADD(s(if(if(z0, z1, z2), x1, x2)), x3) -> c3(A__ADD(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(if(if(z0, z1, z2), x1, x2))) A__ADD(s(if(zero(z0), x1, x2)), x3) -> c3(A__ADD(a__if(a__zero(mark(z0)), x1, x2), mark(x3)), MARK(if(zero(z0), x1, x2))) A__ADD(s(if(prod(z0, z1), x1, x2)), x3) -> c3(A__ADD(a__if(a__prod(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(prod(z0, z1), x1, x2))) A__ADD(s(if(p(z0), x1, x2)), x3) -> c3(A__ADD(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(if(p(z0), x1, x2))) A__ADD(s(if(add(z0, z1), x1, x2)), x3) -> c3(A__ADD(a__if(a__add(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(add(z0, z1), x1, x2))) A__ADD(s(if(s(z0), x1, x2)), x3) -> c3(A__ADD(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(if(s(z0), x1, x2))) A__ADD(s(if(true, x1, x2)), x3) -> c3(A__ADD(a__if(true, x1, x2), mark(x3)), MARK(if(true, x1, x2))) A__ADD(s(if(false, x1, x2)), x3) -> c3(A__ADD(a__if(false, x1, x2), mark(x3)), MARK(if(false, x1, x2))) A__ADD(s(if(x0, z1, z2)), x3) -> c3(MARK(if(x0, z1, z2))) A__ADD(s(if(0, x1, x2)), x3) -> c3(A__ADD(a__if(0, x1, x2), mark(x3))) A__ADD(s(zero(fact(z0))), x1) -> c3(A__ADD(a__zero(a__fact(mark(z0))), mark(x1)), MARK(zero(fact(z0)))) A__ADD(s(zero(if(z0, z1, z2))), x1) -> c3(A__ADD(a__zero(a__if(mark(z0), z1, z2)), mark(x1)), MARK(zero(if(z0, z1, z2)))) A__ADD(s(zero(zero(z0))), x1) -> c3(A__ADD(a__zero(a__zero(mark(z0))), mark(x1)), MARK(zero(zero(z0)))) A__ADD(s(zero(prod(z0, z1))), x1) -> c3(A__ADD(a__zero(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(zero(prod(z0, z1)))) A__ADD(s(zero(p(z0))), x1) -> c3(A__ADD(a__zero(a__p(mark(z0))), mark(x1)), MARK(zero(p(z0)))) A__ADD(s(zero(add(z0, z1))), x1) -> c3(A__ADD(a__zero(a__add(mark(z0), mark(z1))), mark(x1)), MARK(zero(add(z0, z1)))) A__ADD(s(zero(s(z0))), x1) -> c3(A__ADD(a__zero(s(mark(z0))), mark(x1)), MARK(zero(s(z0)))) A__ADD(s(zero(0)), x1) -> c3(A__ADD(a__zero(0), mark(x1)), MARK(zero(0))) A__ADD(s(zero(true)), x1) -> c3(A__ADD(a__zero(true), mark(x1)), MARK(zero(true))) A__ADD(s(zero(false)), x1) -> c3(A__ADD(a__zero(false), mark(x1)), MARK(zero(false))) A__ADD(s(zero(x0)), x1) -> c3(MARK(zero(x0))) A__ADD(s(prod(x0, fact(z0))), x2) -> c3(A__ADD(a__prod(mark(x0), a__fact(mark(z0))), mark(x2)), MARK(prod(x0, fact(z0)))) A__ADD(s(prod(x0, if(z0, z1, z2))), x2) -> c3(A__ADD(a__prod(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(prod(x0, if(z0, z1, z2)))) A__ADD(s(prod(x0, zero(z0))), x2) -> c3(A__ADD(a__prod(mark(x0), a__zero(mark(z0))), mark(x2)), MARK(prod(x0, zero(z0)))) A__ADD(s(prod(x0, prod(z0, z1))), x2) -> c3(A__ADD(a__prod(mark(x0), a__prod(mark(z0), mark(z1))), mark(x2)), MARK(prod(x0, prod(z0, z1)))) A__ADD(s(prod(x0, p(z0))), x2) -> c3(A__ADD(a__prod(mark(x0), a__p(mark(z0))), mark(x2)), MARK(prod(x0, p(z0)))) A__ADD(s(prod(x0, add(z0, z1))), x2) -> c3(A__ADD(a__prod(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(prod(x0, add(z0, z1)))) A__ADD(s(prod(x0, s(z0))), x2) -> c3(A__ADD(a__prod(mark(x0), s(mark(z0))), mark(x2)), MARK(prod(x0, s(z0)))) A__ADD(s(prod(x0, 0)), x2) -> c3(A__ADD(a__prod(mark(x0), 0), mark(x2)), MARK(prod(x0, 0))) A__ADD(s(prod(x0, true)), x2) -> c3(A__ADD(a__prod(mark(x0), true), mark(x2)), MARK(prod(x0, true))) A__ADD(s(prod(x0, false)), x2) -> c3(A__ADD(a__prod(mark(x0), false), mark(x2)), MARK(prod(x0, false))) A__ADD(s(prod(fact(z0), x1)), x2) -> c3(A__ADD(a__prod(a__fact(mark(z0)), mark(x1)), mark(x2)), MARK(prod(fact(z0), x1))) A__ADD(s(prod(if(z0, z1, z2), x1)), x2) -> c3(A__ADD(a__prod(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(prod(if(z0, z1, z2), x1))) A__ADD(s(prod(zero(z0), x1)), x2) -> c3(A__ADD(a__prod(a__zero(mark(z0)), mark(x1)), mark(x2)), MARK(prod(zero(z0), x1))) A__ADD(s(prod(prod(z0, z1), x1)), x2) -> c3(A__ADD(a__prod(a__prod(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(prod(prod(z0, z1), x1))) A__ADD(s(prod(p(z0), x1)), x2) -> c3(A__ADD(a__prod(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(prod(p(z0), x1))) A__ADD(s(prod(add(z0, z1), x1)), x2) -> c3(A__ADD(a__prod(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(prod(add(z0, z1), x1))) A__ADD(s(prod(s(z0), x1)), x2) -> c3(A__ADD(a__prod(s(mark(z0)), mark(x1)), mark(x2)), MARK(prod(s(z0), x1))) A__ADD(s(prod(0, x1)), x2) -> c3(A__ADD(a__prod(0, mark(x1)), mark(x2)), MARK(prod(0, x1))) A__ADD(s(prod(true, x1)), x2) -> c3(A__ADD(a__prod(true, mark(x1)), mark(x2)), MARK(prod(true, x1))) A__ADD(s(prod(false, x1)), x2) -> c3(A__ADD(a__prod(false, mark(x1)), mark(x2)), MARK(prod(false, x1))) A__ADD(s(prod(x0, x1)), x2) -> c3(MARK(prod(x0, x1))) A__ADD(s(p(fact(z0))), x1) -> c3(A__ADD(a__p(a__fact(mark(z0))), mark(x1)), MARK(p(fact(z0)))) A__ADD(s(p(if(z0, z1, z2))), x1) -> c3(A__ADD(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2)))) A__ADD(s(p(zero(z0))), x1) -> c3(A__ADD(a__p(a__zero(mark(z0))), mark(x1)), MARK(p(zero(z0)))) A__ADD(s(p(prod(z0, z1))), x1) -> c3(A__ADD(a__p(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(p(prod(z0, z1)))) A__ADD(s(p(p(z0))), x1) -> c3(A__ADD(a__p(a__p(mark(z0))), mark(x1)), MARK(p(p(z0)))) A__ADD(s(p(add(z0, z1))), x1) -> c3(A__ADD(a__p(a__add(mark(z0), mark(z1))), mark(x1)), MARK(p(add(z0, z1)))) A__ADD(s(p(s(z0))), x1) -> c3(A__ADD(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0)))) A__ADD(s(p(x0)), x1) -> c3(MARK(p(x0))) A__ADD(s(p(0)), x1) -> c3(A__ADD(a__p(0), mark(x1))) A__ADD(s(p(true)), x1) -> c3(A__ADD(a__p(true), mark(x1))) A__ADD(s(p(false)), x1) -> c3(A__ADD(a__p(false), mark(x1))) A__ADD(s(add(x0, fact(z0))), x2) -> c3(A__ADD(a__add(mark(x0), a__fact(mark(z0))), mark(x2)), MARK(add(x0, fact(z0)))) A__ADD(s(add(x0, if(z0, z1, z2))), x2) -> c3(A__ADD(a__add(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(add(x0, if(z0, z1, z2)))) A__ADD(s(add(x0, zero(z0))), x2) -> c3(A__ADD(a__add(mark(x0), a__zero(mark(z0))), mark(x2)), MARK(add(x0, zero(z0)))) A__ADD(s(add(x0, prod(z0, z1))), x2) -> c3(A__ADD(a__add(mark(x0), a__prod(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, prod(z0, z1)))) A__ADD(s(add(x0, p(z0))), x2) -> c3(A__ADD(a__add(mark(x0), a__p(mark(z0))), mark(x2)), MARK(add(x0, p(z0)))) A__ADD(s(add(x0, add(z0, z1))), x2) -> c3(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, add(z0, z1)))) A__ADD(s(add(x0, s(z0))), x2) -> c3(A__ADD(a__add(mark(x0), s(mark(z0))), mark(x2)), MARK(add(x0, s(z0)))) A__ADD(s(add(x0, 0)), x2) -> c3(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(add(x0, 0))) A__ADD(s(add(x0, true)), x2) -> c3(A__ADD(a__add(mark(x0), true), mark(x2)), MARK(add(x0, true))) A__ADD(s(add(x0, false)), x2) -> c3(A__ADD(a__add(mark(x0), false), mark(x2)), MARK(add(x0, false))) A__ADD(s(add(fact(z0), x1)), x2) -> c3(A__ADD(a__add(a__fact(mark(z0)), mark(x1)), mark(x2)), MARK(add(fact(z0), x1))) A__ADD(s(add(if(z0, z1, z2), x1)), x2) -> c3(A__ADD(a__add(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(add(if(z0, z1, z2), x1))) A__ADD(s(add(zero(z0), x1)), x2) -> c3(A__ADD(a__add(a__zero(mark(z0)), mark(x1)), mark(x2)), MARK(add(zero(z0), x1))) A__ADD(s(add(prod(z0, z1), x1)), x2) -> c3(A__ADD(a__add(a__prod(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(prod(z0, z1), x1))) A__ADD(s(add(p(z0), x1)), x2) -> c3(A__ADD(a__add(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(add(p(z0), x1))) A__ADD(s(add(add(z0, z1), x1)), x2) -> c3(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(add(z0, z1), x1))) A__ADD(s(add(s(z0), x1)), x2) -> c3(A__ADD(a__add(s(mark(z0)), mark(x1)), mark(x2)), MARK(add(s(z0), x1))) A__ADD(s(add(0, x1)), x2) -> c3(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(add(0, x1))) A__ADD(s(add(true, x1)), x2) -> c3(A__ADD(a__add(true, mark(x1)), mark(x2)), MARK(add(true, x1))) A__ADD(s(add(false, x1)), x2) -> c3(A__ADD(a__add(false, mark(x1)), mark(x2)), MARK(add(false, x1))) A__ADD(s(add(x0, x1)), x2) -> c3(MARK(add(x0, x1))) A__ADD(s(s(fact(z0))), x1) -> c3(A__ADD(s(a__fact(mark(z0))), mark(x1)), MARK(s(fact(z0)))) A__ADD(s(s(if(z0, z1, z2))), x1) -> c3(A__ADD(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(s(if(z0, z1, z2)))) A__ADD(s(s(zero(z0))), x1) -> c3(A__ADD(s(a__zero(mark(z0))), mark(x1)), MARK(s(zero(z0)))) A__ADD(s(s(prod(z0, z1))), x1) -> c3(A__ADD(s(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(s(prod(z0, z1)))) A__ADD(s(s(p(z0))), x1) -> c3(A__ADD(s(a__p(mark(z0))), mark(x1)), MARK(s(p(z0)))) A__ADD(s(s(add(z0, z1))), x1) -> c3(A__ADD(s(a__add(mark(z0), mark(z1))), mark(x1)), MARK(s(add(z0, z1)))) A__ADD(s(s(s(z0))), x1) -> c3(A__ADD(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__ADD(s(s(0)), x1) -> c3(A__ADD(s(0), mark(x1)), MARK(s(0))) A__ADD(s(s(true)), x1) -> c3(A__ADD(s(true), mark(x1)), MARK(s(true))) A__ADD(s(s(false)), x1) -> c3(A__ADD(s(false), mark(x1)), MARK(s(false))) A__ADD(s(s(x0)), x1) -> c3(MARK(s(x0))) A__ADD(s(x0), fact(x1)) -> c4(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(fact(x1))) A__ADD(s(x0), fact(x1)) -> c4(A__ADD(mark(x0), fact(mark(x1))), MARK(fact(x1))) A__ADD(s(x0), fact(fact(z0))) -> c4(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(fact(fact(z0)))) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c4(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(fact(if(z0, z1, z2)))) A__ADD(s(x0), fact(zero(z0))) -> c4(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(fact(zero(z0)))) A__ADD(s(x0), fact(prod(z0, z1))) -> c4(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(fact(prod(z0, z1)))) A__ADD(s(x0), fact(p(z0))) -> c4(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(fact(p(z0)))) A__ADD(s(x0), fact(add(z0, z1))) -> c4(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(fact(add(z0, z1)))) A__ADD(s(x0), fact(s(z0))) -> c4(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(fact(s(z0)))) A__ADD(s(x0), fact(0)) -> c4(A__ADD(mark(x0), a__fact(0)), MARK(fact(0))) A__ADD(s(x0), fact(true)) -> c4(A__ADD(mark(x0), a__fact(true)), MARK(fact(true))) A__ADD(s(x0), fact(false)) -> c4(A__ADD(mark(x0), a__fact(false)), MARK(fact(false))) A__ADD(s(fact(z0)), fact(x1)) -> c4(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c4(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(zero(z0)), fact(x1)) -> c4(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(p(z0)), fact(x1)) -> c4(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(add(z0, z1)), fact(x1)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(s(z0)), fact(x1)) -> c4(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(0), fact(x1)) -> c4(A__ADD(0, a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(x0), fact(x1)) -> c4(MARK(fact(x1))) A__ADD(s(true), fact(x1)) -> c4(MARK(fact(x1))) A__ADD(s(false), fact(x1)) -> c4(MARK(fact(x1))) A__ADD(s(x0), if(x1, z1, z2)) -> c4(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(if(x1, z1, z2))) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(if(fact(z0), x2, x3))) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(if(if(z0, z1, z2), x2, x3))) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(if(zero(z0), x2, x3))) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(if(prod(z0, z1), x2, x3))) A__ADD(s(x0), if(p(z0), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(if(p(z0), x2, x3))) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(if(add(z0, z1), x2, x3))) A__ADD(s(x0), if(s(z0), x2, x3)) -> c4(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(if(s(z0), x2, x3))) A__ADD(s(x0), if(true, x2, x3)) -> c4(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(if(true, x2, x3))) A__ADD(s(x0), if(false, x2, x3)) -> c4(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(if(false, x2, x3))) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c4(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c4(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c4(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c4(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c4(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(0), if(x1, x2, x3)) -> c4(A__ADD(0, a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(x0), if(0, x2, x3)) -> c4(A__ADD(mark(x0), a__if(0, x2, x3))) A__ADD(s(true), if(x1, x2, x3)) -> c4(MARK(if(x1, x2, x3))) A__ADD(s(false), if(x1, x2, x3)) -> c4(MARK(if(x1, x2, x3))) A__ADD(s(x0), zero(x1)) -> c4(A__ADD(mark(x0), zero(mark(x1))), MARK(zero(x1))) A__ADD(s(x0), zero(fact(z0))) -> c4(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(zero(fact(z0)))) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c4(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(zero(if(z0, z1, z2)))) A__ADD(s(x0), zero(zero(z0))) -> c4(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(zero(zero(z0)))) A__ADD(s(x0), zero(prod(z0, z1))) -> c4(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(zero(prod(z0, z1)))) A__ADD(s(x0), zero(p(z0))) -> c4(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(zero(p(z0)))) A__ADD(s(x0), zero(add(z0, z1))) -> c4(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(zero(add(z0, z1)))) A__ADD(s(x0), zero(s(z0))) -> c4(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(zero(s(z0)))) A__ADD(s(x0), zero(0)) -> c4(A__ADD(mark(x0), a__zero(0)), MARK(zero(0))) A__ADD(s(x0), zero(true)) -> c4(A__ADD(mark(x0), a__zero(true)), MARK(zero(true))) A__ADD(s(x0), zero(false)) -> c4(A__ADD(mark(x0), a__zero(false)), MARK(zero(false))) A__ADD(s(fact(z0)), zero(x1)) -> c4(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c4(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(zero(z0)), zero(x1)) -> c4(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(p(z0)), zero(x1)) -> c4(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(add(z0, z1)), zero(x1)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(s(z0)), zero(x1)) -> c4(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(0), zero(x1)) -> c4(A__ADD(0, a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(x0), zero(x1)) -> c4(MARK(zero(x1))) A__ADD(s(true), zero(x1)) -> c4(MARK(zero(x1))) A__ADD(s(false), zero(x1)) -> c4(MARK(zero(x1))) A__ADD(s(x0), prod(x1, x2)) -> c4(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(x0), prod(x1, fact(z0))) -> c4(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(prod(x1, fact(z0)))) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c4(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(prod(x1, if(z0, z1, z2)))) A__ADD(s(x0), prod(x1, zero(z0))) -> c4(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(prod(x1, zero(z0)))) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c4(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(prod(x1, prod(z0, z1)))) A__ADD(s(x0), prod(x1, p(z0))) -> c4(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(prod(x1, p(z0)))) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c4(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(prod(x1, add(z0, z1)))) A__ADD(s(x0), prod(x1, s(z0))) -> c4(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(prod(x1, s(z0)))) A__ADD(s(x0), prod(x1, 0)) -> c4(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(prod(x1, 0))) A__ADD(s(x0), prod(x1, true)) -> c4(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(prod(x1, true))) A__ADD(s(x0), prod(x1, false)) -> c4(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(prod(x1, false))) A__ADD(s(x0), prod(fact(z0), x2)) -> c4(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(prod(fact(z0), x2))) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c4(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(prod(if(z0, z1, z2), x2))) A__ADD(s(x0), prod(zero(z0), x2)) -> c4(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(prod(zero(z0), x2))) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c4(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(prod(prod(z0, z1), x2))) A__ADD(s(x0), prod(p(z0), x2)) -> c4(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(prod(p(z0), x2))) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c4(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(prod(add(z0, z1), x2))) A__ADD(s(x0), prod(s(z0), x2)) -> c4(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(prod(s(z0), x2))) A__ADD(s(x0), prod(0, x2)) -> c4(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(prod(0, x2))) A__ADD(s(x0), prod(true, x2)) -> c4(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(prod(true, x2))) A__ADD(s(x0), prod(false, x2)) -> c4(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(prod(false, x2))) A__ADD(s(fact(z0)), prod(x1, x2)) -> c4(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c4(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c4(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(p(z0)), prod(x1, x2)) -> c4(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(s(z0)), prod(x1, x2)) -> c4(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(0), prod(x1, x2)) -> c4(A__ADD(0, a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(true), prod(x1, x2)) -> c4(MARK(prod(x1, x2))) A__ADD(s(false), prod(x1, x2)) -> c4(MARK(prod(x1, x2))) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__PROD_2, A__FACT_1 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c27_1, c21_1, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1, c24_2, c25_2, c25_1, c26_2, c26_1, c_2, c_1, c3_2 ---------------------------------------- (227) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__ADD(s(x0), p(z0)) -> c4(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) by A__ADD(s(x0), p(x1)) -> c4(A__ADD(mark(x0), p(mark(x1))), MARK(p(x1))) A__ADD(s(x0), p(fact(z0))) -> c4(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(p(fact(z0)))) A__ADD(s(x0), p(if(z0, z1, z2))) -> c4(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(p(if(z0, z1, z2)))) A__ADD(s(x0), p(zero(z0))) -> c4(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(p(zero(z0)))) A__ADD(s(x0), p(prod(z0, z1))) -> c4(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(p(prod(z0, z1)))) A__ADD(s(x0), p(p(z0))) -> c4(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(p(p(z0)))) A__ADD(s(x0), p(add(z0, z1))) -> c4(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(p(add(z0, z1)))) A__ADD(s(x0), p(s(z0))) -> c4(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(p(s(z0)))) A__ADD(s(x0), p(0)) -> c4(A__ADD(mark(x0), a__p(0)), MARK(p(0))) A__ADD(s(x0), p(true)) -> c4(A__ADD(mark(x0), a__p(true)), MARK(p(true))) A__ADD(s(x0), p(false)) -> c4(A__ADD(mark(x0), a__p(false)), MARK(p(false))) A__ADD(s(fact(z0)), p(x1)) -> c4(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(p(x1))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c4(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(p(x1))) A__ADD(s(zero(z0)), p(x1)) -> c4(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(p(x1))) A__ADD(s(prod(z0, z1)), p(x1)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(p(x1))) A__ADD(s(p(z0)), p(x1)) -> c4(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(x1))) A__ADD(s(add(z0, z1)), p(x1)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(p(x1))) A__ADD(s(s(z0)), p(x1)) -> c4(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(p(x1))) A__ADD(s(0), p(x1)) -> c4(A__ADD(0, a__p(mark(x1))), MARK(p(x1))) A__ADD(s(true), p(x1)) -> c4(A__ADD(true, a__p(mark(x1))), MARK(p(x1))) A__ADD(s(false), p(x1)) -> c4(A__ADD(false, a__p(mark(x1))), MARK(p(x1))) ---------------------------------------- (228) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), 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fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1)))) A__ADD(s(x0), prod(x1, x2)) -> 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x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c4(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c4(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(0), if(x1, x2, x3)) -> c4(A__ADD(0, a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(x0), if(0, x2, x3)) -> c4(A__ADD(mark(x0), a__if(0, x2, x3))) A__ADD(s(true), if(x1, x2, x3)) -> c4(MARK(if(x1, x2, x3))) A__ADD(s(false), if(x1, x2, x3)) -> c4(MARK(if(x1, x2, x3))) A__ADD(s(x0), zero(x1)) -> c4(A__ADD(mark(x0), zero(mark(x1))), MARK(zero(x1))) A__ADD(s(x0), zero(fact(z0))) -> c4(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(zero(fact(z0)))) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c4(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(zero(if(z0, z1, z2)))) A__ADD(s(x0), zero(zero(z0))) -> c4(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(zero(zero(z0)))) A__ADD(s(x0), zero(prod(z0, z1))) -> c4(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(zero(prod(z0, z1)))) A__ADD(s(x0), zero(p(z0))) -> c4(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(zero(p(z0)))) A__ADD(s(x0), zero(add(z0, z1))) -> c4(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(zero(add(z0, z1)))) A__ADD(s(x0), zero(s(z0))) -> c4(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(zero(s(z0)))) A__ADD(s(x0), zero(0)) -> c4(A__ADD(mark(x0), a__zero(0)), MARK(zero(0))) A__ADD(s(x0), zero(true)) -> c4(A__ADD(mark(x0), a__zero(true)), MARK(zero(true))) A__ADD(s(x0), zero(false)) -> c4(A__ADD(mark(x0), a__zero(false)), MARK(zero(false))) A__ADD(s(fact(z0)), zero(x1)) -> c4(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c4(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(zero(z0)), zero(x1)) -> c4(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(p(z0)), zero(x1)) -> c4(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(add(z0, z1)), zero(x1)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(s(z0)), zero(x1)) -> c4(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(0), zero(x1)) -> c4(A__ADD(0, a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(x0), zero(x1)) -> c4(MARK(zero(x1))) A__ADD(s(true), zero(x1)) -> c4(MARK(zero(x1))) A__ADD(s(false), zero(x1)) -> c4(MARK(zero(x1))) A__ADD(s(x0), prod(x1, x2)) -> c4(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(x0), prod(x1, fact(z0))) -> c4(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(prod(x1, fact(z0)))) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c4(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(prod(x1, if(z0, z1, z2)))) A__ADD(s(x0), prod(x1, zero(z0))) -> c4(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(prod(x1, zero(z0)))) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c4(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(prod(x1, prod(z0, z1)))) A__ADD(s(x0), prod(x1, p(z0))) -> c4(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(prod(x1, p(z0)))) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c4(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(prod(x1, add(z0, z1)))) A__ADD(s(x0), prod(x1, s(z0))) -> c4(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(prod(x1, s(z0)))) A__ADD(s(x0), prod(x1, 0)) -> c4(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(prod(x1, 0))) A__ADD(s(x0), prod(x1, true)) -> c4(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(prod(x1, true))) A__ADD(s(x0), prod(x1, false)) -> c4(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(prod(x1, false))) A__ADD(s(x0), prod(fact(z0), x2)) -> c4(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(prod(fact(z0), x2))) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c4(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(prod(if(z0, z1, z2), x2))) A__ADD(s(x0), prod(zero(z0), x2)) -> c4(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(prod(zero(z0), x2))) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c4(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(prod(prod(z0, z1), x2))) A__ADD(s(x0), prod(p(z0), x2)) -> c4(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(prod(p(z0), x2))) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c4(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(prod(add(z0, z1), x2))) A__ADD(s(x0), prod(s(z0), x2)) -> c4(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(prod(s(z0), x2))) A__ADD(s(x0), prod(0, x2)) -> c4(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(prod(0, x2))) A__ADD(s(x0), prod(true, x2)) -> c4(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(prod(true, x2))) A__ADD(s(x0), prod(false, x2)) -> c4(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(prod(false, x2))) A__ADD(s(fact(z0)), prod(x1, x2)) -> c4(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c4(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c4(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(p(z0)), prod(x1, x2)) -> c4(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(s(z0)), prod(x1, x2)) -> c4(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(0), prod(x1, x2)) -> c4(A__ADD(0, a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(true), prod(x1, x2)) -> c4(MARK(prod(x1, x2))) A__ADD(s(false), prod(x1, x2)) -> c4(MARK(prod(x1, x2))) A__ADD(s(x0), p(x1)) -> c4(A__ADD(mark(x0), p(mark(x1))), MARK(p(x1))) A__ADD(s(x0), p(fact(z0))) -> c4(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(p(fact(z0)))) A__ADD(s(x0), p(if(z0, z1, z2))) -> c4(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(p(if(z0, z1, z2)))) A__ADD(s(x0), p(zero(z0))) -> c4(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(p(zero(z0)))) A__ADD(s(x0), p(prod(z0, z1))) -> c4(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(p(prod(z0, z1)))) A__ADD(s(x0), p(p(z0))) -> c4(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(p(p(z0)))) A__ADD(s(x0), p(add(z0, z1))) -> c4(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(p(add(z0, z1)))) A__ADD(s(x0), p(s(z0))) -> c4(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(p(s(z0)))) A__ADD(s(x0), p(0)) -> c4(A__ADD(mark(x0), a__p(0)), MARK(p(0))) A__ADD(s(x0), p(true)) -> c4(A__ADD(mark(x0), a__p(true)), MARK(p(true))) A__ADD(s(x0), p(false)) -> c4(A__ADD(mark(x0), a__p(false)), MARK(p(false))) A__ADD(s(fact(z0)), p(x1)) -> c4(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(p(x1))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c4(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(p(x1))) A__ADD(s(zero(z0)), p(x1)) -> c4(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(p(x1))) A__ADD(s(prod(z0, z1)), p(x1)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(p(x1))) A__ADD(s(p(z0)), p(x1)) -> c4(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(x1))) A__ADD(s(add(z0, z1)), p(x1)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(p(x1))) A__ADD(s(s(z0)), p(x1)) -> c4(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(p(x1))) A__ADD(s(0), p(x1)) -> c4(A__ADD(0, a__p(mark(x1))), MARK(p(x1))) A__ADD(s(true), p(x1)) -> c4(A__ADD(true, a__p(mark(x1))), MARK(p(x1))) A__ADD(s(false), p(x1)) -> c4(A__ADD(false, a__p(mark(x1))), MARK(p(x1))) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), 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prod(fact(z0), x2)) -> c4(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(prod(fact(z0), x2))) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c4(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(prod(if(z0, z1, z2), x2))) A__ADD(s(x0), prod(zero(z0), x2)) -> c4(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(prod(zero(z0), x2))) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c4(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(prod(prod(z0, z1), x2))) A__ADD(s(x0), prod(p(z0), x2)) -> c4(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(prod(p(z0), x2))) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c4(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(prod(add(z0, z1), x2))) A__ADD(s(x0), prod(s(z0), x2)) -> c4(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(prod(s(z0), x2))) A__ADD(s(x0), prod(0, x2)) -> c4(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(prod(0, x2))) A__ADD(s(x0), prod(true, x2)) -> c4(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(prod(true, x2))) A__ADD(s(x0), prod(false, x2)) -> c4(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(prod(false, x2))) A__ADD(s(fact(z0)), prod(x1, x2)) -> c4(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c4(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c4(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(p(z0)), prod(x1, x2)) -> c4(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(s(z0)), prod(x1, x2)) -> c4(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(0), prod(x1, x2)) -> c4(A__ADD(0, a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(true), prod(x1, x2)) -> c4(MARK(prod(x1, x2))) A__ADD(s(false), prod(x1, x2)) -> c4(MARK(prod(x1, x2))) A__ADD(s(x0), p(x1)) -> c4(A__ADD(mark(x0), p(mark(x1))), MARK(p(x1))) A__ADD(s(x0), p(fact(z0))) -> c4(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(p(fact(z0)))) A__ADD(s(x0), p(if(z0, z1, z2))) -> c4(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(p(if(z0, z1, z2)))) A__ADD(s(x0), p(zero(z0))) -> c4(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(p(zero(z0)))) A__ADD(s(x0), p(prod(z0, z1))) -> c4(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(p(prod(z0, z1)))) A__ADD(s(x0), p(p(z0))) -> c4(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(p(p(z0)))) A__ADD(s(x0), p(add(z0, z1))) -> c4(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(p(add(z0, z1)))) A__ADD(s(x0), p(s(z0))) -> c4(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(p(s(z0)))) A__ADD(s(x0), p(0)) -> c4(A__ADD(mark(x0), a__p(0)), MARK(p(0))) A__ADD(s(x0), p(true)) -> c4(A__ADD(mark(x0), a__p(true)), MARK(p(true))) A__ADD(s(x0), p(false)) -> c4(A__ADD(mark(x0), a__p(false)), MARK(p(false))) A__ADD(s(fact(z0)), p(x1)) -> c4(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(p(x1))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c4(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(p(x1))) A__ADD(s(zero(z0)), p(x1)) -> c4(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(p(x1))) A__ADD(s(prod(z0, z1)), p(x1)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(p(x1))) A__ADD(s(p(z0)), p(x1)) -> c4(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(x1))) A__ADD(s(add(z0, z1)), p(x1)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(p(x1))) A__ADD(s(s(z0)), p(x1)) -> c4(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(p(x1))) A__ADD(s(0), p(x1)) -> c4(A__ADD(0, a__p(mark(x1))), MARK(p(x1))) A__ADD(s(true), p(x1)) -> c4(A__ADD(true, a__p(mark(x1))), MARK(p(x1))) A__ADD(s(false), p(x1)) -> c4(A__ADD(false, a__p(mark(x1))), MARK(p(x1))) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__PROD_2, A__FACT_1 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c27_1, c21_1, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1, c24_2, c25_2, c25_1, c26_2, c26_1, c_2, c_1, c3_2 ---------------------------------------- (229) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing tuple parts ---------------------------------------- (230) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1)))) A__ADD(s(x0), prod(x1, x2)) -> c3(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), prod(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, p(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, s(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, 0)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), prod(x1, true)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(x0)) A__ADD(s(x0), prod(x1, false)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(x0)) A__ADD(s(x0), prod(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(p(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(0, x2)) -> c3(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(true, x2)) -> c3(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(false, x2)) -> c3(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), prod(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2)))) A__ADD(s(x0), p(x1)) -> c3(A__ADD(mark(x0), p(mark(x1))), MARK(x0)) A__ADD(s(x0), p(fact(z0))) -> c3(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), p(zero(z0))) -> c3(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(p(z0))) -> c3(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(add(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(s(z0))) -> c3(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(0)) -> c3(A__ADD(mark(x0), a__p(0)), MARK(x0)) A__ADD(s(x0), p(true)) -> c3(A__ADD(mark(x0), a__p(true)), MARK(x0)) A__ADD(s(x0), p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1)))) A__ADD(s(x0), add(x1, x2)) -> c3(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), add(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), add(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, p(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, s(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, 0)) -> c3(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), add(x1, true)) -> c3(A__ADD(mark(x0), a__add(mark(x1), true)), MARK(x0)) A__ADD(s(x0), add(x1, false)) -> c3(A__ADD(mark(x0), a__add(mark(x1), false)), MARK(x0)) A__ADD(s(x0), add(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), add(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(p(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(s(z0), x2)) -> c3(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(0, x2)) -> c3(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) A__ADD(s(x0), add(true, x2)) -> c3(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(x0)) A__ADD(s(x0), add(false, x2)) -> c3(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), add(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), add(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), 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c4(A__ADD(0, a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(x0), if(0, x2, x3)) -> c4(A__ADD(mark(x0), a__if(0, x2, x3))) A__ADD(s(true), if(x1, x2, x3)) -> c4(MARK(if(x1, x2, x3))) A__ADD(s(false), if(x1, x2, x3)) -> c4(MARK(if(x1, x2, x3))) A__ADD(s(x0), zero(x1)) -> c4(A__ADD(mark(x0), zero(mark(x1))), MARK(zero(x1))) A__ADD(s(x0), zero(fact(z0))) -> c4(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(zero(fact(z0)))) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c4(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(zero(if(z0, z1, z2)))) A__ADD(s(x0), zero(zero(z0))) -> c4(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(zero(zero(z0)))) A__ADD(s(x0), zero(prod(z0, z1))) -> c4(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(zero(prod(z0, z1)))) A__ADD(s(x0), zero(p(z0))) -> c4(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(zero(p(z0)))) A__ADD(s(x0), zero(add(z0, z1))) -> c4(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(zero(add(z0, z1)))) A__ADD(s(x0), zero(s(z0))) -> c4(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(zero(s(z0)))) A__ADD(s(x0), zero(0)) -> c4(A__ADD(mark(x0), a__zero(0)), MARK(zero(0))) A__ADD(s(x0), zero(true)) -> c4(A__ADD(mark(x0), a__zero(true)), MARK(zero(true))) A__ADD(s(x0), zero(false)) -> c4(A__ADD(mark(x0), a__zero(false)), MARK(zero(false))) A__ADD(s(fact(z0)), zero(x1)) -> c4(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c4(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(zero(z0)), zero(x1)) -> c4(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(p(z0)), zero(x1)) -> c4(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(add(z0, z1)), zero(x1)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(s(z0)), zero(x1)) -> c4(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(0), zero(x1)) -> c4(A__ADD(0, a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(x0), zero(x1)) -> c4(MARK(zero(x1))) A__ADD(s(true), zero(x1)) -> c4(MARK(zero(x1))) A__ADD(s(false), zero(x1)) -> c4(MARK(zero(x1))) A__ADD(s(x0), prod(x1, x2)) -> c4(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(x0), prod(x1, fact(z0))) -> c4(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(prod(x1, fact(z0)))) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c4(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(prod(x1, if(z0, z1, z2)))) A__ADD(s(x0), prod(x1, zero(z0))) -> c4(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(prod(x1, zero(z0)))) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c4(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(prod(x1, prod(z0, z1)))) A__ADD(s(x0), prod(x1, p(z0))) -> c4(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(prod(x1, p(z0)))) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c4(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(prod(x1, add(z0, z1)))) A__ADD(s(x0), prod(x1, s(z0))) -> c4(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(prod(x1, s(z0)))) A__ADD(s(x0), prod(x1, 0)) -> c4(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(prod(x1, 0))) A__ADD(s(x0), prod(x1, true)) -> c4(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(prod(x1, true))) A__ADD(s(x0), prod(x1, false)) -> c4(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(prod(x1, false))) A__ADD(s(x0), prod(fact(z0), x2)) -> c4(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(prod(fact(z0), x2))) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c4(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(prod(if(z0, z1, z2), x2))) A__ADD(s(x0), prod(zero(z0), x2)) -> c4(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(prod(zero(z0), x2))) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c4(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(prod(prod(z0, z1), x2))) A__ADD(s(x0), prod(p(z0), x2)) -> c4(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(prod(p(z0), x2))) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c4(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(prod(add(z0, z1), x2))) A__ADD(s(x0), prod(s(z0), x2)) -> c4(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(prod(s(z0), x2))) A__ADD(s(x0), prod(0, x2)) -> c4(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(prod(0, x2))) A__ADD(s(x0), prod(true, x2)) -> c4(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(prod(true, x2))) A__ADD(s(x0), prod(false, x2)) -> c4(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(prod(false, x2))) A__ADD(s(fact(z0)), prod(x1, x2)) -> c4(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c4(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c4(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(p(z0)), prod(x1, x2)) -> c4(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(s(z0)), prod(x1, x2)) -> c4(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(0), prod(x1, x2)) -> c4(A__ADD(0, a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(true), prod(x1, x2)) -> c4(MARK(prod(x1, x2))) A__ADD(s(false), prod(x1, x2)) -> c4(MARK(prod(x1, x2))) A__ADD(s(x0), p(x1)) -> c4(A__ADD(mark(x0), p(mark(x1))), MARK(p(x1))) A__ADD(s(x0), p(fact(z0))) -> c4(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(p(fact(z0)))) A__ADD(s(x0), p(if(z0, z1, z2))) -> c4(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(p(if(z0, z1, z2)))) A__ADD(s(x0), p(zero(z0))) -> c4(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(p(zero(z0)))) A__ADD(s(x0), p(prod(z0, z1))) -> c4(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(p(prod(z0, z1)))) A__ADD(s(x0), p(p(z0))) -> c4(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(p(p(z0)))) A__ADD(s(x0), p(add(z0, z1))) -> c4(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(p(add(z0, z1)))) A__ADD(s(x0), p(s(z0))) -> c4(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(p(s(z0)))) A__ADD(s(fact(z0)), p(x1)) -> c4(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(p(x1))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c4(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(p(x1))) A__ADD(s(zero(z0)), p(x1)) -> c4(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(p(x1))) A__ADD(s(prod(z0, z1)), p(x1)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(p(x1))) A__ADD(s(p(z0)), p(x1)) -> c4(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(x1))) A__ADD(s(add(z0, z1)), p(x1)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(p(x1))) A__ADD(s(s(z0)), p(x1)) -> c4(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(p(x1))) A__ADD(s(0), p(x1)) -> c4(A__ADD(0, a__p(mark(x1))), MARK(p(x1))) A__ADD(s(x0), p(0)) -> c4(A__ADD(mark(x0), a__p(0))) A__ADD(s(x0), p(true)) -> c4(A__ADD(mark(x0), a__p(true))) A__ADD(s(x0), p(false)) -> c4(A__ADD(mark(x0), a__p(false))) A__ADD(s(true), p(x1)) -> c4(MARK(p(x1))) A__ADD(s(false), p(x1)) -> c4(MARK(p(x1))) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), 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z2)), MARK(if(x1, z1, z2))) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(if(fact(z0), x2, x3))) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(if(if(z0, z1, z2), x2, x3))) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(if(zero(z0), x2, x3))) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(if(prod(z0, z1), x2, x3))) A__ADD(s(x0), if(p(z0), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(if(p(z0), x2, x3))) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(if(add(z0, z1), x2, x3))) A__ADD(s(x0), if(s(z0), x2, x3)) -> c4(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(if(s(z0), x2, x3))) A__ADD(s(x0), if(true, x2, x3)) -> c4(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(if(true, x2, x3))) A__ADD(s(x0), if(false, x2, x3)) -> c4(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(if(false, x2, x3))) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c4(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c4(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c4(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c4(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c4(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(0), if(x1, x2, x3)) -> c4(A__ADD(0, a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(x0), if(0, x2, x3)) -> c4(A__ADD(mark(x0), a__if(0, x2, x3))) A__ADD(s(true), if(x1, x2, x3)) -> c4(MARK(if(x1, x2, x3))) A__ADD(s(false), if(x1, x2, x3)) -> c4(MARK(if(x1, x2, x3))) A__ADD(s(x0), zero(x1)) -> c4(A__ADD(mark(x0), zero(mark(x1))), MARK(zero(x1))) A__ADD(s(x0), zero(fact(z0))) -> c4(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(zero(fact(z0)))) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c4(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(zero(if(z0, z1, z2)))) A__ADD(s(x0), zero(zero(z0))) -> c4(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(zero(zero(z0)))) A__ADD(s(x0), zero(prod(z0, z1))) -> c4(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(zero(prod(z0, z1)))) A__ADD(s(x0), zero(p(z0))) -> c4(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(zero(p(z0)))) A__ADD(s(x0), zero(add(z0, z1))) -> c4(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(zero(add(z0, z1)))) A__ADD(s(x0), zero(s(z0))) -> c4(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(zero(s(z0)))) A__ADD(s(x0), zero(0)) -> c4(A__ADD(mark(x0), a__zero(0)), MARK(zero(0))) A__ADD(s(x0), zero(true)) -> c4(A__ADD(mark(x0), a__zero(true)), MARK(zero(true))) A__ADD(s(x0), zero(false)) -> c4(A__ADD(mark(x0), a__zero(false)), MARK(zero(false))) A__ADD(s(fact(z0)), zero(x1)) -> c4(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c4(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(zero(z0)), zero(x1)) -> c4(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(p(z0)), zero(x1)) -> c4(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(add(z0, z1)), zero(x1)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(s(z0)), zero(x1)) -> c4(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(0), zero(x1)) -> c4(A__ADD(0, a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(x0), zero(x1)) -> c4(MARK(zero(x1))) A__ADD(s(true), zero(x1)) -> c4(MARK(zero(x1))) A__ADD(s(false), zero(x1)) -> c4(MARK(zero(x1))) A__ADD(s(x0), prod(x1, x2)) -> c4(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(x0), prod(x1, fact(z0))) -> c4(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(prod(x1, fact(z0)))) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c4(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(prod(x1, if(z0, z1, z2)))) A__ADD(s(x0), prod(x1, zero(z0))) -> c4(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(prod(x1, zero(z0)))) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c4(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(prod(x1, prod(z0, z1)))) A__ADD(s(x0), prod(x1, p(z0))) -> c4(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(prod(x1, p(z0)))) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c4(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(prod(x1, add(z0, z1)))) A__ADD(s(x0), prod(x1, s(z0))) -> c4(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(prod(x1, s(z0)))) A__ADD(s(x0), prod(x1, 0)) -> c4(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(prod(x1, 0))) A__ADD(s(x0), prod(x1, true)) -> c4(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(prod(x1, true))) A__ADD(s(x0), prod(x1, false)) -> c4(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(prod(x1, false))) A__ADD(s(x0), prod(fact(z0), x2)) -> c4(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(prod(fact(z0), x2))) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c4(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(prod(if(z0, z1, z2), x2))) A__ADD(s(x0), prod(zero(z0), x2)) -> c4(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(prod(zero(z0), x2))) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c4(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(prod(prod(z0, z1), x2))) A__ADD(s(x0), prod(p(z0), x2)) -> c4(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(prod(p(z0), x2))) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c4(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(prod(add(z0, z1), x2))) A__ADD(s(x0), prod(s(z0), x2)) -> c4(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(prod(s(z0), x2))) A__ADD(s(x0), prod(0, x2)) -> c4(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(prod(0, x2))) A__ADD(s(x0), prod(true, x2)) -> c4(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(prod(true, x2))) A__ADD(s(x0), prod(false, x2)) -> c4(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(prod(false, x2))) A__ADD(s(fact(z0)), prod(x1, x2)) -> c4(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c4(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c4(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(p(z0)), prod(x1, x2)) -> c4(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(s(z0)), prod(x1, x2)) -> c4(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(0), prod(x1, x2)) -> c4(A__ADD(0, a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(true), prod(x1, x2)) -> c4(MARK(prod(x1, x2))) A__ADD(s(false), prod(x1, x2)) -> c4(MARK(prod(x1, x2))) A__ADD(s(x0), p(x1)) -> c4(A__ADD(mark(x0), p(mark(x1))), MARK(p(x1))) A__ADD(s(x0), p(fact(z0))) -> c4(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(p(fact(z0)))) A__ADD(s(x0), p(if(z0, z1, z2))) -> c4(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(p(if(z0, z1, z2)))) A__ADD(s(x0), p(zero(z0))) -> c4(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(p(zero(z0)))) A__ADD(s(x0), p(prod(z0, z1))) -> c4(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(p(prod(z0, z1)))) A__ADD(s(x0), p(p(z0))) -> c4(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(p(p(z0)))) A__ADD(s(x0), p(add(z0, z1))) -> c4(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(p(add(z0, z1)))) A__ADD(s(x0), p(s(z0))) -> c4(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(p(s(z0)))) A__ADD(s(fact(z0)), p(x1)) -> c4(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(p(x1))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c4(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(p(x1))) A__ADD(s(zero(z0)), p(x1)) -> c4(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(p(x1))) A__ADD(s(prod(z0, z1)), p(x1)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(p(x1))) A__ADD(s(p(z0)), p(x1)) -> c4(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(x1))) A__ADD(s(add(z0, z1)), p(x1)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(p(x1))) A__ADD(s(s(z0)), p(x1)) -> c4(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(p(x1))) A__ADD(s(0), p(x1)) -> c4(A__ADD(0, a__p(mark(x1))), MARK(p(x1))) A__ADD(s(x0), p(0)) -> c4(A__ADD(mark(x0), a__p(0))) A__ADD(s(x0), p(true)) -> c4(A__ADD(mark(x0), a__p(true))) A__ADD(s(x0), p(false)) -> c4(A__ADD(mark(x0), a__p(false))) A__ADD(s(true), p(x1)) -> c4(MARK(p(x1))) A__ADD(s(false), p(x1)) -> c4(MARK(p(x1))) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__PROD_2, A__FACT_1 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c27_1, c21_1, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1, c24_2, c25_2, c25_1, c26_2, c26_1, c_2, c_1, c3_2 ---------------------------------------- (231) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__ADD(s(x0), add(z0, z1)) -> c4(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) by A__ADD(s(x0), add(x1, x2)) -> c4(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(add(x1, x2))) A__ADD(s(x0), add(x1, fact(z0))) -> c4(A__ADD(mark(x0), a__add(mark(x1), a__fact(mark(z0)))), MARK(add(x1, fact(z0)))) A__ADD(s(x0), add(x1, if(z0, z1, z2))) -> c4(A__ADD(mark(x0), a__add(mark(x1), a__if(mark(z0), z1, z2))), MARK(add(x1, if(z0, z1, z2)))) A__ADD(s(x0), add(x1, zero(z0))) -> c4(A__ADD(mark(x0), a__add(mark(x1), a__zero(mark(z0)))), MARK(add(x1, zero(z0)))) A__ADD(s(x0), add(x1, prod(z0, z1))) -> c4(A__ADD(mark(x0), a__add(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(add(x1, prod(z0, z1)))) A__ADD(s(x0), add(x1, p(z0))) -> c4(A__ADD(mark(x0), a__add(mark(x1), a__p(mark(z0)))), MARK(add(x1, p(z0)))) A__ADD(s(x0), add(x1, add(z0, z1))) -> c4(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(add(x1, add(z0, z1)))) A__ADD(s(x0), add(x1, s(z0))) -> c4(A__ADD(mark(x0), a__add(mark(x1), s(mark(z0)))), MARK(add(x1, s(z0)))) A__ADD(s(x0), add(x1, 0)) -> c4(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(add(x1, 0))) A__ADD(s(x0), add(x1, true)) -> c4(A__ADD(mark(x0), a__add(mark(x1), true)), MARK(add(x1, true))) A__ADD(s(x0), add(x1, false)) -> c4(A__ADD(mark(x0), a__add(mark(x1), false)), MARK(add(x1, false))) A__ADD(s(x0), add(fact(z0), x2)) -> c4(A__ADD(mark(x0), a__add(a__fact(mark(z0)), mark(x2))), MARK(add(fact(z0), x2))) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c4(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(add(if(z0, z1, z2), x2))) A__ADD(s(x0), add(zero(z0), x2)) -> c4(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(add(zero(z0), x2))) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c4(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(add(prod(z0, z1), x2))) A__ADD(s(x0), add(p(z0), x2)) -> c4(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(add(p(z0), x2))) A__ADD(s(x0), add(add(z0, z1), x2)) -> c4(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(add(add(z0, z1), x2))) A__ADD(s(x0), add(s(z0), x2)) -> c4(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(add(s(z0), x2))) A__ADD(s(x0), add(0, x2)) -> c4(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(add(0, x2))) A__ADD(s(x0), add(true, x2)) -> c4(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(add(true, x2))) A__ADD(s(x0), add(false, x2)) -> c4(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(add(false, x2))) A__ADD(s(fact(z0)), add(x1, x2)) -> c4(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c4(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c4(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) A__ADD(s(p(z0)), add(x1, x2)) -> c4(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) A__ADD(s(s(z0)), add(x1, x2)) -> c4(A__ADD(s(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) A__ADD(s(0), add(x1, x2)) -> c4(A__ADD(0, a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) A__ADD(s(true), add(x1, x2)) -> c4(A__ADD(true, a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) A__ADD(s(false), add(x1, x2)) -> c4(A__ADD(false, a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) ---------------------------------------- (232) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1)))) A__ADD(s(x0), prod(x1, x2)) -> c3(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), prod(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, p(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, s(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, 0)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), prod(x1, true)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(x0)) A__ADD(s(x0), prod(x1, false)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(x0)) A__ADD(s(x0), prod(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(p(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(0, x2)) -> c3(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(true, x2)) -> c3(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(false, x2)) -> c3(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), prod(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2)))) A__ADD(s(x0), p(x1)) -> c3(A__ADD(mark(x0), p(mark(x1))), MARK(x0)) A__ADD(s(x0), p(fact(z0))) -> c3(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), p(zero(z0))) -> c3(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(p(z0))) -> c3(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(add(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(s(z0))) -> c3(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(0)) -> c3(A__ADD(mark(x0), a__p(0)), MARK(x0)) A__ADD(s(x0), p(true)) -> c3(A__ADD(mark(x0), a__p(true)), MARK(x0)) A__ADD(s(x0), p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1)))) A__ADD(s(x0), add(x1, x2)) -> c3(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), add(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), add(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, p(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, s(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, 0)) -> c3(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), add(x1, true)) -> c3(A__ADD(mark(x0), a__add(mark(x1), true)), MARK(x0)) A__ADD(s(x0), add(x1, false)) -> c3(A__ADD(mark(x0), a__add(mark(x1), false)), MARK(x0)) A__ADD(s(x0), add(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), add(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(p(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(s(z0), x2)) -> c3(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(0, x2)) -> c3(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) A__ADD(s(x0), add(true, x2)) -> c3(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(x0)) A__ADD(s(x0), add(false, x2)) -> c3(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), add(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), add(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), add(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__add(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), add(x1, x2)) -> c3(A__ADD(0, a__add(mark(x1), mark(x2)))) A__ADD(s(x0), s(fact(z0))) -> c3(A__ADD(mark(x0), s(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), s(zero(z0))) -> c3(A__ADD(mark(x0), s(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(prod(z0, z1))) -> c3(A__ADD(mark(x0), s(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(p(z0))) -> c3(A__ADD(mark(x0), s(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(add(z0, z1))) -> c3(A__ADD(mark(x0), s(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(s(z0))) -> c3(A__ADD(mark(x0), s(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(0)) -> c3(A__ADD(mark(x0), s(0)), MARK(x0)) A__ADD(s(x0), s(true)) -> c3(A__ADD(mark(x0), s(true)), MARK(x0)) A__ADD(s(x0), s(false)) -> c3(A__ADD(mark(x0), s(false)), MARK(x0)) A__ADD(s(fact(z0)), s(x1)) -> c3(A__ADD(a__fact(mark(z0)), s(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), s(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), s(x1)) -> c3(A__ADD(a__zero(mark(z0)), s(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), s(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), s(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), s(x1)) -> c3(A__ADD(a__p(mark(z0)), s(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), s(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), s(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), s(x1)) -> c3(A__ADD(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__ADD(s(0), s(x1)) -> c3(A__ADD(0, s(mark(x1)))) A__ADD(s(fact(z0)), 0) -> c3(A__ADD(a__fact(mark(z0)), 0), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), 0) -> c3(A__ADD(a__if(mark(z0), z1, z2), 0), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), 0) -> c3(A__ADD(a__zero(mark(z0)), 0), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), 0) -> 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mark(x2))), MARK(add(if(z0, z1, z2), x2))) A__ADD(s(x0), add(zero(z0), x2)) -> c4(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(add(zero(z0), x2))) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c4(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(add(prod(z0, z1), x2))) A__ADD(s(x0), add(p(z0), x2)) -> c4(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(add(p(z0), x2))) A__ADD(s(x0), add(add(z0, z1), x2)) -> c4(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(add(add(z0, z1), x2))) A__ADD(s(x0), add(s(z0), x2)) -> c4(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(add(s(z0), x2))) A__ADD(s(x0), add(0, x2)) -> c4(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(add(0, x2))) A__ADD(s(x0), add(true, x2)) -> c4(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(add(true, x2))) A__ADD(s(x0), add(false, x2)) -> c4(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(add(false, x2))) A__ADD(s(fact(z0)), add(x1, x2)) -> c4(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c4(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c4(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) A__ADD(s(p(z0)), add(x1, x2)) -> c4(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) A__ADD(s(s(z0)), add(x1, x2)) -> c4(A__ADD(s(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) A__ADD(s(0), add(x1, x2)) -> c4(A__ADD(0, a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) A__ADD(s(true), add(x1, x2)) -> c4(A__ADD(true, a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) A__ADD(s(false), add(x1, x2)) -> c4(A__ADD(false, a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1)))) A__ADD(s(x0), prod(x1, x2)) -> c3(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), prod(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, p(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, s(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, 0)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), prod(x1, true)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(x0)) A__ADD(s(x0), prod(x1, false)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(x0)) A__ADD(s(x0), prod(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(p(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(0, x2)) -> c3(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(true, x2)) -> c3(A__ADD(mark(x0), a__prod(true, mark(x2))), 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A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1)))) A__ADD(s(x0), add(x1, x2)) -> c3(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), add(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), add(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, p(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, s(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, 0)) -> c3(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), add(x1, true)) -> c3(A__ADD(mark(x0), a__add(mark(x1), true)), MARK(x0)) A__ADD(s(x0), add(x1, false)) -> c3(A__ADD(mark(x0), a__add(mark(x1), false)), MARK(x0)) A__ADD(s(x0), add(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), add(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(p(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(s(z0), x2)) -> c3(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(0, x2)) -> c3(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) A__ADD(s(x0), add(true, x2)) -> c3(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(x0)) A__ADD(s(x0), add(false, x2)) -> c3(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), add(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), add(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), add(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__add(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), add(x1, x2)) -> c3(A__ADD(0, a__add(mark(x1), mark(x2)))) A__ADD(s(x0), s(fact(z0))) -> c3(A__ADD(mark(x0), s(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), s(zero(z0))) -> c3(A__ADD(mark(x0), s(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(prod(z0, z1))) -> c3(A__ADD(mark(x0), s(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(p(z0))) -> c3(A__ADD(mark(x0), s(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(add(z0, z1))) -> c3(A__ADD(mark(x0), s(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(s(z0))) -> c3(A__ADD(mark(x0), s(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(0)) -> c3(A__ADD(mark(x0), s(0)), MARK(x0)) A__ADD(s(x0), s(true)) -> c3(A__ADD(mark(x0), s(true)), MARK(x0)) A__ADD(s(x0), s(false)) -> c3(A__ADD(mark(x0), s(false)), MARK(x0)) A__ADD(s(fact(z0)), s(x1)) -> c3(A__ADD(a__fact(mark(z0)), s(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), s(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), s(x1)) -> c3(A__ADD(a__zero(mark(z0)), s(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), s(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), s(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), s(x1)) -> c3(A__ADD(a__p(mark(z0)), s(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), s(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), s(mark(x1))), 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c3(A__ADD(a__prod(a__zero(mark(z0)), mark(x1)), mark(x2)), MARK(prod(zero(z0), x1))) A__ADD(s(prod(prod(z0, z1), x1)), x2) -> c3(A__ADD(a__prod(a__prod(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(prod(prod(z0, z1), x1))) A__ADD(s(prod(p(z0), x1)), x2) -> c3(A__ADD(a__prod(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(prod(p(z0), x1))) A__ADD(s(prod(add(z0, z1), x1)), x2) -> c3(A__ADD(a__prod(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(prod(add(z0, z1), x1))) A__ADD(s(prod(s(z0), x1)), x2) -> c3(A__ADD(a__prod(s(mark(z0)), mark(x1)), mark(x2)), MARK(prod(s(z0), x1))) A__ADD(s(prod(0, x1)), x2) -> c3(A__ADD(a__prod(0, mark(x1)), mark(x2)), MARK(prod(0, x1))) A__ADD(s(prod(true, x1)), x2) -> c3(A__ADD(a__prod(true, mark(x1)), mark(x2)), MARK(prod(true, x1))) A__ADD(s(prod(false, x1)), x2) -> c3(A__ADD(a__prod(false, mark(x1)), mark(x2)), MARK(prod(false, x1))) A__ADD(s(prod(x0, x1)), x2) -> c3(MARK(prod(x0, x1))) A__ADD(s(p(fact(z0))), x1) -> c3(A__ADD(a__p(a__fact(mark(z0))), mark(x1)), MARK(p(fact(z0)))) A__ADD(s(p(if(z0, z1, z2))), x1) -> c3(A__ADD(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2)))) A__ADD(s(p(zero(z0))), x1) -> c3(A__ADD(a__p(a__zero(mark(z0))), mark(x1)), MARK(p(zero(z0)))) A__ADD(s(p(prod(z0, z1))), x1) -> c3(A__ADD(a__p(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(p(prod(z0, z1)))) A__ADD(s(p(p(z0))), x1) -> c3(A__ADD(a__p(a__p(mark(z0))), mark(x1)), MARK(p(p(z0)))) A__ADD(s(p(add(z0, z1))), x1) -> c3(A__ADD(a__p(a__add(mark(z0), mark(z1))), mark(x1)), MARK(p(add(z0, z1)))) A__ADD(s(p(s(z0))), x1) -> c3(A__ADD(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0)))) A__ADD(s(p(x0)), x1) -> c3(MARK(p(x0))) A__ADD(s(p(0)), x1) -> c3(A__ADD(a__p(0), mark(x1))) A__ADD(s(p(true)), x1) -> c3(A__ADD(a__p(true), mark(x1))) A__ADD(s(p(false)), x1) -> c3(A__ADD(a__p(false), mark(x1))) A__ADD(s(add(x0, fact(z0))), x2) -> c3(A__ADD(a__add(mark(x0), a__fact(mark(z0))), mark(x2)), MARK(add(x0, fact(z0)))) A__ADD(s(add(x0, if(z0, z1, z2))), x2) -> c3(A__ADD(a__add(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(add(x0, if(z0, z1, z2)))) A__ADD(s(add(x0, zero(z0))), x2) -> c3(A__ADD(a__add(mark(x0), a__zero(mark(z0))), mark(x2)), MARK(add(x0, zero(z0)))) A__ADD(s(add(x0, prod(z0, z1))), x2) -> c3(A__ADD(a__add(mark(x0), a__prod(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, prod(z0, z1)))) A__ADD(s(add(x0, p(z0))), x2) -> c3(A__ADD(a__add(mark(x0), a__p(mark(z0))), mark(x2)), MARK(add(x0, p(z0)))) A__ADD(s(add(x0, add(z0, z1))), x2) -> c3(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, add(z0, z1)))) A__ADD(s(add(x0, s(z0))), x2) -> c3(A__ADD(a__add(mark(x0), s(mark(z0))), mark(x2)), MARK(add(x0, s(z0)))) A__ADD(s(add(x0, 0)), x2) -> c3(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(add(x0, 0))) A__ADD(s(add(x0, true)), x2) -> c3(A__ADD(a__add(mark(x0), true), mark(x2)), MARK(add(x0, true))) A__ADD(s(add(x0, false)), x2) -> c3(A__ADD(a__add(mark(x0), false), mark(x2)), MARK(add(x0, false))) A__ADD(s(add(fact(z0), x1)), x2) -> c3(A__ADD(a__add(a__fact(mark(z0)), mark(x1)), mark(x2)), MARK(add(fact(z0), x1))) A__ADD(s(add(if(z0, z1, z2), x1)), x2) -> c3(A__ADD(a__add(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(add(if(z0, z1, z2), x1))) A__ADD(s(add(zero(z0), x1)), x2) -> c3(A__ADD(a__add(a__zero(mark(z0)), mark(x1)), mark(x2)), MARK(add(zero(z0), x1))) A__ADD(s(add(prod(z0, z1), x1)), x2) -> c3(A__ADD(a__add(a__prod(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(prod(z0, z1), x1))) A__ADD(s(add(p(z0), x1)), x2) -> c3(A__ADD(a__add(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(add(p(z0), x1))) A__ADD(s(add(add(z0, z1), x1)), x2) -> c3(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(add(z0, z1), x1))) A__ADD(s(add(s(z0), x1)), x2) -> c3(A__ADD(a__add(s(mark(z0)), mark(x1)), mark(x2)), MARK(add(s(z0), x1))) A__ADD(s(add(0, x1)), x2) -> c3(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(add(0, x1))) A__ADD(s(add(true, x1)), x2) -> c3(A__ADD(a__add(true, mark(x1)), mark(x2)), MARK(add(true, x1))) A__ADD(s(add(false, x1)), x2) -> c3(A__ADD(a__add(false, mark(x1)), mark(x2)), MARK(add(false, x1))) A__ADD(s(add(x0, x1)), x2) -> c3(MARK(add(x0, x1))) A__ADD(s(s(fact(z0))), x1) -> c3(A__ADD(s(a__fact(mark(z0))), mark(x1)), MARK(s(fact(z0)))) A__ADD(s(s(if(z0, z1, z2))), x1) -> c3(A__ADD(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(s(if(z0, z1, z2)))) A__ADD(s(s(zero(z0))), x1) -> c3(A__ADD(s(a__zero(mark(z0))), mark(x1)), MARK(s(zero(z0)))) A__ADD(s(s(prod(z0, z1))), x1) -> c3(A__ADD(s(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(s(prod(z0, z1)))) A__ADD(s(s(p(z0))), x1) -> c3(A__ADD(s(a__p(mark(z0))), mark(x1)), MARK(s(p(z0)))) A__ADD(s(s(add(z0, z1))), x1) -> c3(A__ADD(s(a__add(mark(z0), mark(z1))), mark(x1)), MARK(s(add(z0, z1)))) A__ADD(s(s(s(z0))), x1) -> c3(A__ADD(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__ADD(s(s(0)), x1) -> c3(A__ADD(s(0), mark(x1)), MARK(s(0))) A__ADD(s(s(true)), x1) -> c3(A__ADD(s(true), mark(x1)), MARK(s(true))) A__ADD(s(s(false)), x1) -> c3(A__ADD(s(false), mark(x1)), MARK(s(false))) A__ADD(s(s(x0)), x1) -> c3(MARK(s(x0))) A__ADD(s(x0), fact(x1)) -> c4(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(fact(x1))) A__ADD(s(x0), fact(x1)) -> c4(A__ADD(mark(x0), fact(mark(x1))), MARK(fact(x1))) A__ADD(s(x0), fact(fact(z0))) -> c4(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(fact(fact(z0)))) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c4(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(fact(if(z0, z1, z2)))) A__ADD(s(x0), fact(zero(z0))) -> c4(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(fact(zero(z0)))) A__ADD(s(x0), fact(prod(z0, z1))) -> c4(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(fact(prod(z0, z1)))) A__ADD(s(x0), fact(p(z0))) -> c4(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(fact(p(z0)))) A__ADD(s(x0), fact(add(z0, z1))) -> c4(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), 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fact(x1)) -> c4(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(0), fact(x1)) -> c4(A__ADD(0, a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(x0), fact(x1)) -> c4(MARK(fact(x1))) A__ADD(s(true), fact(x1)) -> c4(MARK(fact(x1))) A__ADD(s(false), fact(x1)) -> c4(MARK(fact(x1))) A__ADD(s(x0), if(x1, z1, z2)) -> c4(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(if(x1, z1, z2))) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(if(fact(z0), x2, x3))) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(if(if(z0, z1, z2), x2, x3))) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(if(zero(z0), x2, x3))) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(if(prod(z0, z1), x2, x3))) A__ADD(s(x0), if(p(z0), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(if(p(z0), x2, x3))) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(if(add(z0, z1), x2, x3))) A__ADD(s(x0), if(s(z0), x2, x3)) -> c4(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(if(s(z0), x2, x3))) A__ADD(s(x0), if(true, x2, x3)) -> c4(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(if(true, x2, x3))) A__ADD(s(x0), if(false, x2, x3)) -> c4(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(if(false, x2, x3))) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c4(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c4(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c4(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c4(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c4(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(0), if(x1, x2, x3)) -> c4(A__ADD(0, a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(x0), if(0, x2, x3)) -> c4(A__ADD(mark(x0), a__if(0, x2, x3))) A__ADD(s(true), if(x1, x2, x3)) -> c4(MARK(if(x1, x2, x3))) A__ADD(s(false), if(x1, x2, x3)) -> c4(MARK(if(x1, x2, x3))) A__ADD(s(x0), zero(x1)) -> c4(A__ADD(mark(x0), zero(mark(x1))), MARK(zero(x1))) A__ADD(s(x0), zero(fact(z0))) -> c4(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(zero(fact(z0)))) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c4(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(zero(if(z0, z1, z2)))) A__ADD(s(x0), zero(zero(z0))) -> c4(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(zero(zero(z0)))) A__ADD(s(x0), zero(prod(z0, z1))) -> c4(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(zero(prod(z0, z1)))) A__ADD(s(x0), zero(p(z0))) -> c4(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(zero(p(z0)))) A__ADD(s(x0), zero(add(z0, z1))) -> c4(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(zero(add(z0, z1)))) A__ADD(s(x0), zero(s(z0))) -> c4(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(zero(s(z0)))) A__ADD(s(x0), zero(0)) -> c4(A__ADD(mark(x0), a__zero(0)), MARK(zero(0))) A__ADD(s(x0), zero(true)) -> c4(A__ADD(mark(x0), a__zero(true)), MARK(zero(true))) A__ADD(s(x0), zero(false)) -> c4(A__ADD(mark(x0), a__zero(false)), MARK(zero(false))) A__ADD(s(fact(z0)), zero(x1)) -> c4(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c4(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(zero(z0)), zero(x1)) -> c4(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(p(z0)), zero(x1)) -> c4(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(add(z0, z1)), zero(x1)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(s(z0)), zero(x1)) -> c4(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(0), zero(x1)) -> c4(A__ADD(0, a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(x0), zero(x1)) -> c4(MARK(zero(x1))) A__ADD(s(true), zero(x1)) -> c4(MARK(zero(x1))) A__ADD(s(false), zero(x1)) -> c4(MARK(zero(x1))) A__ADD(s(x0), prod(x1, x2)) -> c4(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(x0), prod(x1, fact(z0))) -> c4(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(prod(x1, fact(z0)))) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c4(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(prod(x1, if(z0, z1, z2)))) A__ADD(s(x0), prod(x1, zero(z0))) -> c4(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(prod(x1, zero(z0)))) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c4(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(prod(x1, prod(z0, z1)))) A__ADD(s(x0), prod(x1, p(z0))) -> c4(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(prod(x1, p(z0)))) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c4(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(prod(x1, add(z0, z1)))) A__ADD(s(x0), prod(x1, s(z0))) -> c4(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(prod(x1, s(z0)))) A__ADD(s(x0), prod(x1, 0)) -> c4(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(prod(x1, 0))) A__ADD(s(x0), prod(x1, true)) -> c4(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(prod(x1, true))) A__ADD(s(x0), prod(x1, false)) -> c4(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(prod(x1, false))) A__ADD(s(x0), prod(fact(z0), x2)) -> c4(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(prod(fact(z0), x2))) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c4(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(prod(if(z0, z1, z2), x2))) A__ADD(s(x0), prod(zero(z0), x2)) -> c4(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(prod(zero(z0), x2))) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c4(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(prod(prod(z0, z1), x2))) A__ADD(s(x0), prod(p(z0), x2)) -> c4(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(prod(p(z0), x2))) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c4(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(prod(add(z0, z1), x2))) A__ADD(s(x0), prod(s(z0), x2)) -> c4(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(prod(s(z0), x2))) A__ADD(s(x0), prod(0, x2)) -> c4(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(prod(0, x2))) A__ADD(s(x0), prod(true, x2)) -> c4(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(prod(true, x2))) A__ADD(s(x0), prod(false, x2)) -> c4(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(prod(false, x2))) A__ADD(s(fact(z0)), prod(x1, x2)) -> c4(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c4(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c4(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(p(z0)), prod(x1, x2)) -> c4(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(s(z0)), prod(x1, x2)) -> c4(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(0), prod(x1, x2)) -> c4(A__ADD(0, a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(true), prod(x1, x2)) -> c4(MARK(prod(x1, x2))) A__ADD(s(false), prod(x1, x2)) -> c4(MARK(prod(x1, x2))) A__ADD(s(x0), p(x1)) -> c4(A__ADD(mark(x0), p(mark(x1))), MARK(p(x1))) A__ADD(s(x0), p(fact(z0))) -> c4(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(p(fact(z0)))) A__ADD(s(x0), p(if(z0, z1, z2))) -> c4(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(p(if(z0, z1, z2)))) A__ADD(s(x0), p(zero(z0))) -> c4(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(p(zero(z0)))) A__ADD(s(x0), p(prod(z0, z1))) -> c4(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(p(prod(z0, z1)))) A__ADD(s(x0), p(p(z0))) -> c4(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(p(p(z0)))) A__ADD(s(x0), p(add(z0, z1))) -> c4(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(p(add(z0, z1)))) A__ADD(s(x0), p(s(z0))) -> c4(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(p(s(z0)))) A__ADD(s(fact(z0)), p(x1)) -> c4(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(p(x1))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c4(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(p(x1))) A__ADD(s(zero(z0)), p(x1)) -> c4(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(p(x1))) A__ADD(s(prod(z0, z1)), p(x1)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(p(x1))) A__ADD(s(p(z0)), p(x1)) -> c4(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(x1))) A__ADD(s(add(z0, z1)), p(x1)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(p(x1))) A__ADD(s(s(z0)), p(x1)) -> c4(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(p(x1))) A__ADD(s(0), p(x1)) -> c4(A__ADD(0, a__p(mark(x1))), MARK(p(x1))) A__ADD(s(x0), p(0)) -> c4(A__ADD(mark(x0), a__p(0))) A__ADD(s(x0), p(true)) -> c4(A__ADD(mark(x0), a__p(true))) A__ADD(s(x0), p(false)) -> c4(A__ADD(mark(x0), a__p(false))) A__ADD(s(true), p(x1)) -> c4(MARK(p(x1))) A__ADD(s(false), p(x1)) -> c4(MARK(p(x1))) A__ADD(s(x0), add(x1, x2)) -> c4(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(add(x1, x2))) A__ADD(s(x0), add(x1, fact(z0))) -> c4(A__ADD(mark(x0), a__add(mark(x1), a__fact(mark(z0)))), MARK(add(x1, fact(z0)))) A__ADD(s(x0), add(x1, if(z0, z1, z2))) -> c4(A__ADD(mark(x0), a__add(mark(x1), a__if(mark(z0), z1, z2))), MARK(add(x1, if(z0, z1, z2)))) A__ADD(s(x0), add(x1, zero(z0))) -> c4(A__ADD(mark(x0), a__add(mark(x1), a__zero(mark(z0)))), MARK(add(x1, zero(z0)))) A__ADD(s(x0), add(x1, prod(z0, z1))) -> c4(A__ADD(mark(x0), a__add(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(add(x1, prod(z0, z1)))) A__ADD(s(x0), add(x1, p(z0))) -> c4(A__ADD(mark(x0), a__add(mark(x1), a__p(mark(z0)))), MARK(add(x1, p(z0)))) A__ADD(s(x0), add(x1, add(z0, z1))) -> c4(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(add(x1, add(z0, z1)))) A__ADD(s(x0), add(x1, s(z0))) -> c4(A__ADD(mark(x0), a__add(mark(x1), s(mark(z0)))), MARK(add(x1, s(z0)))) A__ADD(s(x0), add(x1, 0)) -> c4(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(add(x1, 0))) A__ADD(s(x0), add(x1, true)) -> c4(A__ADD(mark(x0), a__add(mark(x1), true)), MARK(add(x1, true))) A__ADD(s(x0), add(x1, false)) -> c4(A__ADD(mark(x0), a__add(mark(x1), false)), MARK(add(x1, false))) A__ADD(s(x0), add(fact(z0), x2)) -> c4(A__ADD(mark(x0), a__add(a__fact(mark(z0)), mark(x2))), MARK(add(fact(z0), x2))) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c4(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(add(if(z0, z1, z2), x2))) A__ADD(s(x0), add(zero(z0), x2)) -> c4(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(add(zero(z0), x2))) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c4(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(add(prod(z0, z1), x2))) A__ADD(s(x0), add(p(z0), x2)) -> c4(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(add(p(z0), x2))) A__ADD(s(x0), add(add(z0, z1), x2)) -> c4(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(add(add(z0, z1), x2))) A__ADD(s(x0), add(s(z0), x2)) -> c4(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(add(s(z0), x2))) A__ADD(s(x0), add(0, x2)) -> c4(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(add(0, x2))) A__ADD(s(x0), add(true, x2)) -> c4(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(add(true, x2))) A__ADD(s(x0), add(false, x2)) -> c4(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(add(false, x2))) A__ADD(s(fact(z0)), add(x1, x2)) -> c4(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c4(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c4(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) A__ADD(s(p(z0)), add(x1, x2)) -> c4(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) A__ADD(s(s(z0)), add(x1, x2)) -> c4(A__ADD(s(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) A__ADD(s(0), add(x1, x2)) -> c4(A__ADD(0, a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) A__ADD(s(true), add(x1, x2)) -> c4(A__ADD(true, a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) A__ADD(s(false), add(x1, x2)) -> c4(A__ADD(false, a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__PROD_2, A__FACT_1 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c27_1, c21_1, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1, c24_2, c25_2, c25_1, c26_2, c26_1, c_2, c_1, c3_2 ---------------------------------------- (233) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (234) Obligation: Complexity Dependency Tuples Problem Rules: a__fact(z0) -> a__if(a__zero(mark(z0)), s(0), prod(z0, fact(p(z0)))) a__fact(z0) -> fact(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__prod(0, z0) -> 0 a__prod(s(z0), z1) -> a__add(mark(z1), a__prod(mark(z0), mark(z1))) a__prod(z0, z1) -> prod(z0, z1) a__if(true, z0, z1) -> mark(z0) a__if(false, z0, z1) -> mark(z1) a__if(z0, z1, z2) -> if(z0, z1, z2) a__zero(0) -> true a__zero(s(z0)) -> false a__zero(z0) -> zero(z0) a__p(s(z0)) -> mark(z0) a__p(z0) -> p(z0) mark(fact(z0)) -> a__fact(mark(z0)) mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) mark(zero(z0)) -> a__zero(mark(z0)) mark(prod(z0, z1)) -> a__prod(mark(z0), mark(z1)) mark(p(z0)) -> a__p(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(true) -> true mark(false) -> false Tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1)))) A__ADD(s(x0), prod(x1, x2)) -> c3(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), prod(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, p(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, s(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, 0)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), prod(x1, true)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(x0)) A__ADD(s(x0), prod(x1, false)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(x0)) A__ADD(s(x0), prod(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(p(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(0, x2)) -> c3(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(true, x2)) -> c3(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(false, x2)) -> c3(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), prod(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), prod(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), prod(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), prod(x1, x2)) -> c3(A__ADD(0, a__prod(mark(x1), mark(x2)))) A__ADD(s(x0), p(x1)) -> c3(A__ADD(mark(x0), p(mark(x1))), MARK(x0)) A__ADD(s(x0), p(fact(z0))) -> c3(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), p(zero(z0))) -> c3(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(p(z0))) -> c3(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(add(z0, z1))) -> c3(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), p(s(z0))) -> c3(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), p(0)) -> c3(A__ADD(mark(x0), a__p(0)), MARK(x0)) A__ADD(s(x0), p(true)) -> c3(A__ADD(mark(x0), a__p(true)), MARK(x0)) A__ADD(s(x0), p(false)) -> c3(A__ADD(mark(x0), a__p(false)), MARK(x0)) A__ADD(s(fact(z0)), p(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1)))) A__ADD(s(x0), add(x1, x2)) -> c3(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), add(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), add(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, p(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, s(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, 0)) -> c3(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), add(x1, true)) -> c3(A__ADD(mark(x0), a__add(mark(x1), true)), MARK(x0)) A__ADD(s(x0), add(x1, false)) -> c3(A__ADD(mark(x0), a__add(mark(x1), false)), MARK(x0)) A__ADD(s(x0), add(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), add(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(p(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(s(z0), x2)) -> c3(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(0, x2)) -> c3(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) A__ADD(s(x0), add(true, x2)) -> c3(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(x0)) A__ADD(s(x0), add(false, x2)) -> c3(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), add(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), add(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), add(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__add(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), add(x1, x2)) -> c3(A__ADD(0, a__add(mark(x1), mark(x2)))) A__ADD(s(x0), s(fact(z0))) -> c3(A__ADD(mark(x0), s(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), s(zero(z0))) -> c3(A__ADD(mark(x0), s(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(prod(z0, z1))) -> c3(A__ADD(mark(x0), s(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(p(z0))) -> c3(A__ADD(mark(x0), s(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(add(z0, z1))) -> c3(A__ADD(mark(x0), s(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(s(z0))) -> c3(A__ADD(mark(x0), s(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(0)) -> c3(A__ADD(mark(x0), s(0)), MARK(x0)) A__ADD(s(x0), s(true)) -> c3(A__ADD(mark(x0), s(true)), MARK(x0)) A__ADD(s(x0), s(false)) -> c3(A__ADD(mark(x0), s(false)), MARK(x0)) A__ADD(s(fact(z0)), s(x1)) -> c3(A__ADD(a__fact(mark(z0)), s(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), s(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), s(x1)) -> c3(A__ADD(a__zero(mark(z0)), s(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), s(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), s(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), s(x1)) -> c3(A__ADD(a__p(mark(z0)), s(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), s(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), s(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), s(x1)) -> c3(A__ADD(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__ADD(s(0), s(x1)) -> c3(A__ADD(0, s(mark(x1)))) A__ADD(s(fact(z0)), 0) -> c3(A__ADD(a__fact(mark(z0)), 0), MARK(fact(z0))) 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MARK(add(fact(z0), x2))) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c4(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(add(if(z0, z1, z2), x2))) A__ADD(s(x0), add(zero(z0), x2)) -> c4(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(add(zero(z0), x2))) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c4(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(add(prod(z0, z1), x2))) A__ADD(s(x0), add(p(z0), x2)) -> c4(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(add(p(z0), x2))) A__ADD(s(x0), add(add(z0, z1), x2)) -> c4(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(add(add(z0, z1), x2))) A__ADD(s(x0), add(s(z0), x2)) -> c4(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(add(s(z0), x2))) A__ADD(s(x0), add(0, x2)) -> c4(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(add(0, x2))) A__ADD(s(x0), add(true, x2)) -> c4(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(add(true, x2))) A__ADD(s(x0), add(false, x2)) -> c4(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(add(false, x2))) A__ADD(s(fact(z0)), add(x1, x2)) -> c4(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c4(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c4(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) A__ADD(s(p(z0)), add(x1, x2)) -> c4(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) A__ADD(s(s(z0)), add(x1, x2)) -> c4(A__ADD(s(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) A__ADD(s(0), add(x1, x2)) -> c4(A__ADD(0, a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) A__ADD(s(true), add(x1, x2)) -> c4(MARK(add(x1, x2))) A__ADD(s(false), add(x1, x2)) -> c4(MARK(add(x1, x2))) S tuples: A__ADD(0, z0) -> c2(MARK(z0)) A__IF(true, z0, z1) -> c11(MARK(z0)) A__IF(false, z0, z1) -> c12(MARK(z1)) A__P(s(z0)) -> c17(MARK(z0)) MARK(fact(z0)) -> c19(A__FACT(mark(z0)), MARK(z0)) MARK(s(z0)) -> c27(MARK(z0)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(0), x1) -> c3(A__ADD(0, mark(x1))) A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) A__ADD(s(zero(z0)), x1) -> c4(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(prod(z0, z1)), x1) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(p(z0)), x1) -> c4(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c4(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c4(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c4(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c4(A__ADD(mark(x0), 0)) A__ADD(s(x0), true) -> c4(A__ADD(mark(x0), true)) A__ADD(s(x0), false) -> c4(A__ADD(mark(x0), false)) A__ADD(s(true), x1) -> c4(MARK(x1)) A__ADD(s(false), x1) -> c4(MARK(x1)) A__PROD(s(x0), x1) -> c7(A__ADD(mark(x1), prod(mark(x0), mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c7(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(p(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c7(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__PROD(s(s(z0)), x1) -> c7(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), MARK(x1)) A__PROD(s(0), x1) -> c7(A__ADD(mark(x1), a__prod(0, mark(x1))), MARK(x1)) A__PROD(s(true), x1) -> c7(A__ADD(mark(x1), a__prod(true, mark(x1))), MARK(x1)) A__PROD(s(false), x1) -> c7(A__ADD(mark(x1), a__prod(false, mark(x1))), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c7(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c7(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c7(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c7(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c7(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c7(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c7(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), MARK(s(z0))) A__PROD(s(x0), 0) -> c7(A__ADD(mark(0), a__prod(mark(x0), 0))) A__PROD(s(x0), true) -> c7(A__ADD(mark(true), a__prod(mark(x0), true))) A__PROD(s(x0), false) -> c7(A__ADD(mark(false), a__prod(mark(x0), false))) A__PROD(s(x0), 0) -> c7(A__ADD(0, a__prod(mark(x0), mark(0)))) A__PROD(s(x0), x1) -> c8(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x0)) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(x0), true) -> c8(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(fact(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(fact(z0))) A__PROD(s(if(z0, z1, z2)), x1) -> c8(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) A__PROD(s(zero(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(zero(z0))) A__PROD(s(prod(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(prod(z0, z1))) A__PROD(s(p(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(p(z0))) A__PROD(s(add(z0, z1)), x1) -> c8(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(add(z0, z1))) A__PROD(s(s(z0)), x1) -> c8(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(s(z0))) A__PROD(s(x0), fact(z0)) -> c8(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(x0)) A__PROD(s(x0), if(z0, z1, z2)) -> c8(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) A__PROD(s(x0), zero(z0)) -> c8(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(x0)) A__PROD(s(x0), prod(z0, z1)) -> c8(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(x0)) A__PROD(s(x0), p(z0)) -> c8(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(x0)) A__PROD(s(x0), add(z0, z1)) -> c8(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(x0)) A__PROD(s(x0), s(z0)) -> c8(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(x0)) A__PROD(s(x0), 0) -> c8(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0)), MARK(x0)) A__PROD(s(0), x1) -> c8(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1))) A__PROD(s(true), x1) -> c8(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1))) A__PROD(s(false), x1) -> c8(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1))) A__PROD(s(x0), true) -> c8(A__PROD(mark(x0), mark(true)), MARK(x0)) A__PROD(s(x0), false) -> c8(A__PROD(mark(x0), mark(false)), MARK(x0)) A__PROD(s(x0), x1) -> c9(A__ADD(mark(x1), prod(mark(x0), mark(x1))), A__PROD(mark(x0), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(mark(fact(z0)), a__prod(mark(x0), a__fact(mark(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(mark(if(z0, z1, z2)), a__prod(mark(x0), a__if(mark(z0), z1, z2))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(mark(zero(z0)), a__prod(mark(x0), a__zero(mark(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(mark(prod(z0, z1)), a__prod(mark(x0), a__prod(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(mark(p(z0)), a__prod(mark(x0), a__p(mark(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(mark(add(z0, z1)), a__prod(mark(x0), a__add(mark(z0), mark(z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(mark(s(z0)), a__prod(mark(x0), s(mark(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(fact(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__fact(mark(z0)), mark(x1))), A__PROD(mark(fact(z0)), mark(x1)), MARK(x1)) A__PROD(s(if(z0, z1, z2)), x1) -> c9(A__ADD(mark(x1), a__prod(a__if(mark(z0), z1, z2), mark(x1))), A__PROD(mark(if(z0, z1, z2)), mark(x1)), MARK(x1)) A__PROD(s(zero(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__zero(mark(z0)), mark(x1))), A__PROD(mark(zero(z0)), mark(x1)), MARK(x1)) A__PROD(s(prod(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__prod(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(prod(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(p(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(a__p(mark(z0)), mark(x1))), A__PROD(mark(p(z0)), mark(x1)), MARK(x1)) A__PROD(s(add(z0, z1)), x1) -> c9(A__ADD(mark(x1), a__prod(a__add(mark(z0), mark(z1)), mark(x1))), A__PROD(mark(add(z0, z1)), mark(x1)), MARK(x1)) A__PROD(s(s(z0)), x1) -> c9(A__ADD(mark(x1), a__prod(s(mark(z0)), mark(x1))), A__PROD(mark(s(z0)), mark(x1)), MARK(x1)) A__PROD(s(0), x1) -> c9(A__ADD(mark(x1), a__prod(0, mark(x1))), A__PROD(mark(0), mark(x1)), MARK(x1)) A__PROD(s(true), x1) -> c9(A__ADD(mark(x1), a__prod(true, mark(x1))), A__PROD(mark(true), mark(x1)), MARK(x1)) A__PROD(s(false), x1) -> c9(A__ADD(mark(x1), a__prod(false, mark(x1))), A__PROD(mark(false), mark(x1)), MARK(x1)) A__PROD(s(x0), fact(z0)) -> c9(A__ADD(a__fact(mark(z0)), a__prod(mark(x0), mark(fact(z0)))), A__PROD(mark(x0), mark(fact(z0))), MARK(fact(z0))) A__PROD(s(x0), if(z0, z1, z2)) -> c9(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x0), mark(if(z0, z1, z2)))), A__PROD(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2))) A__PROD(s(x0), zero(z0)) -> c9(A__ADD(a__zero(mark(z0)), a__prod(mark(x0), mark(zero(z0)))), A__PROD(mark(x0), mark(zero(z0))), MARK(zero(z0))) A__PROD(s(x0), prod(z0, z1)) -> c9(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x0), mark(prod(z0, z1)))), A__PROD(mark(x0), mark(prod(z0, z1))), MARK(prod(z0, z1))) A__PROD(s(x0), p(z0)) -> c9(A__ADD(a__p(mark(z0)), a__prod(mark(x0), mark(p(z0)))), A__PROD(mark(x0), mark(p(z0))), MARK(p(z0))) A__PROD(s(x0), add(z0, z1)) -> c9(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x0), mark(add(z0, z1)))), A__PROD(mark(x0), mark(add(z0, z1))), MARK(add(z0, z1))) A__PROD(s(x0), s(z0)) -> c9(A__ADD(s(mark(z0)), a__prod(mark(x0), mark(s(z0)))), A__PROD(mark(x0), mark(s(z0))), MARK(s(z0))) A__PROD(s(x0), 0) -> c9(A__ADD(mark(0), a__prod(mark(x0), 0)), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__ADD(mark(true), a__prod(mark(x0), true)), A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__ADD(mark(false), a__prod(mark(x0), false)), A__PROD(mark(x0), mark(false))) A__PROD(s(x0), 0) -> c9(A__ADD(0, a__prod(mark(x0), mark(0))), A__PROD(mark(x0), mark(0))) A__PROD(s(x0), true) -> c9(A__PROD(mark(x0), mark(true))) A__PROD(s(x0), false) -> c9(A__PROD(mark(x0), mark(false))) MARK(if(fact(z0), x1, x2)) -> c20(A__IF(a__fact(mark(z0)), x1, x2), MARK(fact(z0))) MARK(if(if(z0, z1, z2), x1, x2)) -> c20(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2))) MARK(if(zero(z0), x1, x2)) -> c20(A__IF(a__zero(mark(z0)), x1, x2), MARK(zero(z0))) MARK(if(prod(z0, z1), x1, x2)) -> c20(A__IF(a__prod(mark(z0), mark(z1)), x1, x2), MARK(prod(z0, z1))) MARK(if(p(z0), x1, x2)) -> c20(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0))) MARK(if(add(z0, z1), x1, x2)) -> c20(A__IF(a__add(mark(z0), mark(z1)), x1, x2), MARK(add(z0, z1))) MARK(if(s(z0), x1, x2)) -> c20(MARK(s(z0))) MARK(if(true, x1, x2)) -> c20(A__IF(true, x1, x2)) MARK(if(false, x1, x2)) -> c20(A__IF(false, x1, x2)) MARK(prod(x0, fact(z0))) -> c22(A__PROD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(prod(x0, if(z0, z1, z2))) -> c22(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(prod(x0, zero(z0))) -> c22(A__PROD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(prod(x0, prod(z0, z1))) -> c22(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, p(z0))) -> c22(A__PROD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(prod(x0, add(z0, z1))) -> c22(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(prod(x0, s(z0))) -> c22(A__PROD(mark(x0), s(mark(z0))), MARK(x0)) MARK(prod(x0, 0)) -> c22(A__PROD(mark(x0), 0), MARK(x0)) MARK(prod(x0, true)) -> c22(A__PROD(mark(x0), true), MARK(x0)) MARK(prod(x0, false)) -> c22(A__PROD(mark(x0), false), MARK(x0)) MARK(prod(fact(z0), x1)) -> c22(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(prod(if(z0, z1, z2), x1)) -> c22(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(prod(zero(z0), x1)) -> c22(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(prod(prod(z0, z1), x1)) -> c22(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(prod(p(z0), x1)) -> c22(A__PROD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(prod(add(z0, z1), x1)) -> c22(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(prod(s(z0), x1)) -> c22(A__PROD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(prod(x0, fact(z0))) -> c23(A__PROD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(prod(x0, if(z0, z1, z2))) -> c23(A__PROD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(prod(x0, zero(z0))) -> c23(A__PROD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(prod(x0, prod(z0, z1))) -> c23(A__PROD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(prod(x0, p(z0))) -> c23(A__PROD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(prod(x0, add(z0, z1))) -> c23(A__PROD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(prod(x0, s(z0))) -> c23(A__PROD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(prod(fact(z0), x1)) -> c23(A__PROD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(if(z0, z1, z2), x1)) -> c23(A__PROD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(prod(zero(z0), x1)) -> c23(A__PROD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(prod(z0, z1), x1)) -> c23(A__PROD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(p(z0), x1)) -> c23(A__PROD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(add(z0, z1), x1)) -> c23(A__PROD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(prod(s(z0), x1)) -> c23(A__PROD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(prod(x0, 0)) -> c23(A__PROD(mark(x0), 0)) MARK(prod(x0, true)) -> c23(A__PROD(mark(x0), true)) MARK(prod(x0, false)) -> c23(A__PROD(mark(x0), false)) MARK(prod(0, x1)) -> c23(MARK(x1)) MARK(prod(true, x1)) -> c23(MARK(x1)) MARK(prod(false, x1)) -> c23(MARK(x1)) MARK(p(fact(z0))) -> c24(A__P(a__fact(mark(z0))), MARK(fact(z0))) MARK(p(if(z0, z1, z2))) -> c24(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(p(zero(z0))) -> c24(A__P(a__zero(mark(z0))), MARK(zero(z0))) MARK(p(prod(z0, z1))) -> c24(A__P(a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(p(p(z0))) -> c24(A__P(a__p(mark(z0))), MARK(p(z0))) MARK(p(add(z0, z1))) -> c24(A__P(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(p(s(z0))) -> c24(A__P(s(mark(z0))), MARK(s(z0))) MARK(add(x0, fact(z0))) -> c25(A__ADD(mark(x0), a__fact(mark(z0))), MARK(x0)) MARK(add(x0, if(z0, z1, z2))) -> c25(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) MARK(add(x0, zero(z0))) -> c25(A__ADD(mark(x0), a__zero(mark(z0))), MARK(x0)) MARK(add(x0, prod(z0, z1))) -> c25(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, p(z0))) -> c25(A__ADD(mark(x0), a__p(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c25(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, s(z0))) -> c25(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c25(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, true)) -> c25(A__ADD(mark(x0), true), MARK(x0)) MARK(add(x0, false)) -> c25(A__ADD(mark(x0), false), MARK(x0)) MARK(add(fact(z0), x1)) -> c25(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(fact(z0))) MARK(add(if(z0, z1, z2), x1)) -> c25(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) MARK(add(zero(z0), x1)) -> c25(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(zero(z0))) MARK(add(prod(z0, z1), x1)) -> c25(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(prod(z0, z1))) MARK(add(p(z0), x1)) -> c25(A__ADD(a__p(mark(z0)), mark(x1)), MARK(p(z0))) MARK(add(add(z0, z1), x1)) -> c25(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(s(z0), x1)) -> c25(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c25(A__ADD(0, mark(x1))) MARK(add(x0, fact(z0))) -> c26(A__ADD(mark(x0), a__fact(mark(z0))), MARK(fact(z0))) MARK(add(x0, if(z0, z1, z2))) -> c26(A__ADD(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) MARK(add(x0, zero(z0))) -> c26(A__ADD(mark(x0), a__zero(mark(z0))), MARK(zero(z0))) MARK(add(x0, prod(z0, z1))) -> c26(A__ADD(mark(x0), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) MARK(add(x0, p(z0))) -> c26(A__ADD(mark(x0), a__p(mark(z0))), MARK(p(z0))) MARK(add(x0, add(z0, z1))) -> c26(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, s(z0))) -> c26(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(fact(z0), x1)) -> c26(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) MARK(add(if(z0, z1, z2), x1)) -> c26(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(add(zero(z0), x1)) -> c26(A__ADD(a__zero(mark(z0)), mark(x1)), MARK(x1)) MARK(add(prod(z0, z1), x1)) -> c26(A__ADD(a__prod(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(p(z0), x1)) -> c26(A__ADD(a__p(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c26(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c26(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c26(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c26(A__ADD(mark(x0), 0)) MARK(add(x0, true)) -> c26(A__ADD(mark(x0), true)) MARK(add(x0, false)) -> c26(A__ADD(mark(x0), false)) MARK(add(true, x1)) -> c26(MARK(x1)) MARK(add(false, x1)) -> c26(MARK(x1)) A__FACT(fact(z0)) -> c(A__IF(a__zero(a__fact(mark(z0))), s(0), prod(fact(z0), fact(p(fact(z0))))), MARK(fact(z0))) A__FACT(if(z0, z1, z2)) -> c(A__IF(a__zero(a__if(mark(z0), z1, z2)), s(0), prod(if(z0, z1, z2), fact(p(if(z0, z1, z2))))), MARK(if(z0, z1, z2))) A__FACT(zero(z0)) -> c(A__IF(a__zero(a__zero(mark(z0))), s(0), prod(zero(z0), fact(p(zero(z0))))), MARK(zero(z0))) A__FACT(prod(z0, z1)) -> c(A__IF(a__zero(a__prod(mark(z0), mark(z1))), s(0), prod(prod(z0, z1), fact(p(prod(z0, z1))))), MARK(prod(z0, z1))) A__FACT(p(z0)) -> c(A__IF(a__zero(a__p(mark(z0))), s(0), prod(p(z0), fact(p(p(z0))))), MARK(p(z0))) A__FACT(add(z0, z1)) -> c(A__IF(a__zero(a__add(mark(z0), mark(z1))), s(0), prod(add(z0, z1), fact(p(add(z0, z1))))), MARK(add(z0, z1))) A__FACT(s(z0)) -> c(A__IF(a__zero(s(mark(z0))), s(0), prod(s(z0), fact(p(s(z0))))), MARK(s(z0))) A__FACT(x0) -> c(MARK(x0)) A__FACT(0) -> c(A__IF(a__zero(0), s(0), prod(0, fact(p(0))))) A__FACT(true) -> c(A__IF(a__zero(true), s(0), prod(true, fact(p(true))))) A__FACT(false) -> c(A__IF(a__zero(false), s(0), prod(false, fact(p(false))))) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(x0)) A__ADD(s(x0), fact(x1)) -> c3(A__ADD(mark(x0), fact(mark(x1))), MARK(x0)) A__ADD(s(x0), fact(fact(z0))) -> c3(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), fact(zero(z0))) -> c3(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(p(z0))) -> c3(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(add(z0, z1))) -> c3(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), fact(s(z0))) -> c3(A__ADD(mark(x0), a__fact(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), fact(0)) -> c3(A__ADD(mark(x0), a__fact(0)), MARK(x0)) A__ADD(s(x0), fact(true)) -> c3(A__ADD(mark(x0), a__fact(true)), MARK(x0)) A__ADD(s(x0), fact(false)) -> c3(A__ADD(mark(x0), a__fact(false)), MARK(x0)) A__ADD(s(fact(z0)), fact(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__fact(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), fact(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__fact(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), fact(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__fact(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), fact(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), fact(x1)) -> c3(A__ADD(a__p(mark(z0)), a__fact(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), fact(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__fact(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), fact(x1)) -> c3(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(s(z0))) A__ADD(s(0), fact(x1)) -> c3(A__ADD(0, a__fact(mark(x1)))) A__ADD(s(x0), if(x1, z1, z2)) -> c3(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(x0)) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0)) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(p(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c3(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(s(z0), x2, x3)) -> c3(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0)) A__ADD(s(x0), if(0, x2, x3)) -> c3(A__ADD(mark(x0), a__if(0, x2, x3)), MARK(x0)) A__ADD(s(x0), if(true, x2, x3)) -> c3(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(x0)) A__ADD(s(x0), if(false, x2, x3)) -> c3(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(x0)) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(prod(z0, z1))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c3(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(add(z0, z1))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c3(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0))) A__ADD(s(0), if(x1, x2, x3)) -> c3(A__ADD(0, a__if(mark(x1), x2, x3))) A__ADD(s(x0), zero(x1)) -> c3(A__ADD(mark(x0), zero(mark(x1))), MARK(x0)) A__ADD(s(x0), zero(fact(z0))) -> c3(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), zero(zero(z0))) -> c3(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(prod(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(p(z0))) -> c3(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(add(z0, z1))) -> c3(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), zero(s(z0))) -> c3(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), zero(0)) -> c3(A__ADD(mark(x0), a__zero(0)), MARK(x0)) A__ADD(s(x0), zero(true)) -> c3(A__ADD(mark(x0), a__zero(true)), MARK(x0)) A__ADD(s(x0), zero(false)) -> c3(A__ADD(mark(x0), a__zero(false)), MARK(x0)) A__ADD(s(fact(z0)), zero(x1)) -> c3(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), zero(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), zero(x1)) -> c3(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), zero(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), zero(x1)) -> c3(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(s(z0))) A__ADD(s(0), zero(x1)) -> c3(A__ADD(0, a__zero(mark(x1)))) A__ADD(s(x0), prod(x1, x2)) -> c3(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), prod(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, p(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), prod(x1, s(z0))) -> c3(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), prod(x1, 0)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), prod(x1, true)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(x0)) A__ADD(s(x0), prod(x1, false)) -> c3(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(x0)) A__ADD(s(x0), prod(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(p(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(s(z0), x2)) -> c3(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), prod(0, x2)) -> c3(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(x0)) A__ADD(s(x0), prod(true, x2)) -> c3(A__ADD(mark(x0), a__prod(true, mark(x2))), 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A__ADD(s(if(z0, z1, z2)), p(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), p(x1)) -> c3(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), p(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), p(x1)) -> c3(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), p(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(add(z0, z1))) A__ADD(s(s(z0)), p(x1)) -> c3(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(s(z0))) A__ADD(s(0), p(x1)) -> c3(A__ADD(0, a__p(mark(x1)))) A__ADD(s(x0), add(x1, x2)) -> c3(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) A__ADD(s(x0), add(x1, fact(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, if(z0, z1, z2))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), add(x1, zero(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, prod(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, p(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, add(z0, z1))) -> c3(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), add(x1, s(z0))) -> c3(A__ADD(mark(x0), a__add(mark(x1), s(mark(z0)))), MARK(x0)) A__ADD(s(x0), add(x1, 0)) -> c3(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) A__ADD(s(x0), add(x1, true)) -> c3(A__ADD(mark(x0), a__add(mark(x1), true)), MARK(x0)) A__ADD(s(x0), add(x1, false)) -> c3(A__ADD(mark(x0), a__add(mark(x1), false)), MARK(x0)) A__ADD(s(x0), add(fact(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__fact(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c3(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0)) A__ADD(s(x0), add(zero(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(p(z0), x2)) -> c3(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(add(z0, z1), x2)) -> c3(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(s(z0), x2)) -> c3(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(x0)) A__ADD(s(x0), add(0, x2)) -> c3(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) A__ADD(s(x0), add(true, x2)) -> c3(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(x0)) A__ADD(s(x0), add(false, x2)) -> c3(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(x0)) A__ADD(s(fact(z0)), add(x1, x2)) -> c3(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c3(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c3(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), add(x1, x2)) -> c3(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(p(z0))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) A__ADD(s(s(z0)), add(x1, x2)) -> c3(A__ADD(s(mark(z0)), a__add(mark(x1), mark(x2))), MARK(s(z0))) A__ADD(s(0), add(x1, x2)) -> c3(A__ADD(0, a__add(mark(x1), mark(x2)))) A__ADD(s(x0), s(fact(z0))) -> c3(A__ADD(mark(x0), s(a__fact(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(if(z0, z1, z2))) -> c3(A__ADD(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0)) A__ADD(s(x0), s(zero(z0))) -> c3(A__ADD(mark(x0), s(a__zero(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(prod(z0, z1))) -> c3(A__ADD(mark(x0), s(a__prod(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(p(z0))) -> c3(A__ADD(mark(x0), s(a__p(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(add(z0, z1))) -> c3(A__ADD(mark(x0), s(a__add(mark(z0), mark(z1)))), MARK(x0)) A__ADD(s(x0), s(s(z0))) -> c3(A__ADD(mark(x0), s(s(mark(z0)))), MARK(x0)) A__ADD(s(x0), s(0)) -> c3(A__ADD(mark(x0), s(0)), MARK(x0)) A__ADD(s(x0), s(true)) -> c3(A__ADD(mark(x0), s(true)), MARK(x0)) A__ADD(s(x0), s(false)) -> c3(A__ADD(mark(x0), s(false)), MARK(x0)) A__ADD(s(fact(z0)), s(x1)) -> c3(A__ADD(a__fact(mark(z0)), s(mark(x1))), MARK(fact(z0))) A__ADD(s(if(z0, z1, z2)), s(x1)) -> c3(A__ADD(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2))) A__ADD(s(zero(z0)), s(x1)) -> c3(A__ADD(a__zero(mark(z0)), s(mark(x1))), MARK(zero(z0))) A__ADD(s(prod(z0, z1)), s(x1)) -> c3(A__ADD(a__prod(mark(z0), mark(z1)), s(mark(x1))), MARK(prod(z0, z1))) A__ADD(s(p(z0)), s(x1)) -> c3(A__ADD(a__p(mark(z0)), s(mark(x1))), MARK(p(z0))) A__ADD(s(add(z0, z1)), s(x1)) -> c3(A__ADD(a__add(mark(z0), mark(z1)), s(mark(x1))), 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c3(A__ADD(a__prod(a__zero(mark(z0)), mark(x1)), mark(x2)), MARK(prod(zero(z0), x1))) A__ADD(s(prod(prod(z0, z1), x1)), x2) -> c3(A__ADD(a__prod(a__prod(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(prod(prod(z0, z1), x1))) A__ADD(s(prod(p(z0), x1)), x2) -> c3(A__ADD(a__prod(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(prod(p(z0), x1))) A__ADD(s(prod(add(z0, z1), x1)), x2) -> c3(A__ADD(a__prod(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(prod(add(z0, z1), x1))) A__ADD(s(prod(s(z0), x1)), x2) -> c3(A__ADD(a__prod(s(mark(z0)), mark(x1)), mark(x2)), MARK(prod(s(z0), x1))) A__ADD(s(prod(0, x1)), x2) -> c3(A__ADD(a__prod(0, mark(x1)), mark(x2)), MARK(prod(0, x1))) A__ADD(s(prod(true, x1)), x2) -> c3(A__ADD(a__prod(true, mark(x1)), mark(x2)), MARK(prod(true, x1))) A__ADD(s(prod(false, x1)), x2) -> c3(A__ADD(a__prod(false, mark(x1)), mark(x2)), MARK(prod(false, x1))) A__ADD(s(prod(x0, x1)), x2) -> c3(MARK(prod(x0, x1))) A__ADD(s(p(fact(z0))), x1) -> c3(A__ADD(a__p(a__fact(mark(z0))), mark(x1)), MARK(p(fact(z0)))) A__ADD(s(p(if(z0, z1, z2))), x1) -> c3(A__ADD(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2)))) A__ADD(s(p(zero(z0))), x1) -> c3(A__ADD(a__p(a__zero(mark(z0))), mark(x1)), MARK(p(zero(z0)))) A__ADD(s(p(prod(z0, z1))), x1) -> c3(A__ADD(a__p(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(p(prod(z0, z1)))) A__ADD(s(p(p(z0))), x1) -> c3(A__ADD(a__p(a__p(mark(z0))), mark(x1)), MARK(p(p(z0)))) A__ADD(s(p(add(z0, z1))), x1) -> c3(A__ADD(a__p(a__add(mark(z0), mark(z1))), mark(x1)), MARK(p(add(z0, z1)))) A__ADD(s(p(s(z0))), x1) -> c3(A__ADD(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0)))) A__ADD(s(p(x0)), x1) -> c3(MARK(p(x0))) A__ADD(s(p(0)), x1) -> c3(A__ADD(a__p(0), mark(x1))) A__ADD(s(p(true)), x1) -> c3(A__ADD(a__p(true), mark(x1))) A__ADD(s(p(false)), x1) -> c3(A__ADD(a__p(false), mark(x1))) A__ADD(s(add(x0, fact(z0))), x2) -> c3(A__ADD(a__add(mark(x0), a__fact(mark(z0))), mark(x2)), MARK(add(x0, fact(z0)))) A__ADD(s(add(x0, if(z0, z1, z2))), x2) -> c3(A__ADD(a__add(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(add(x0, if(z0, z1, z2)))) A__ADD(s(add(x0, zero(z0))), x2) -> c3(A__ADD(a__add(mark(x0), a__zero(mark(z0))), mark(x2)), MARK(add(x0, zero(z0)))) A__ADD(s(add(x0, prod(z0, z1))), x2) -> c3(A__ADD(a__add(mark(x0), a__prod(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, prod(z0, z1)))) A__ADD(s(add(x0, p(z0))), x2) -> c3(A__ADD(a__add(mark(x0), a__p(mark(z0))), mark(x2)), MARK(add(x0, p(z0)))) A__ADD(s(add(x0, add(z0, z1))), x2) -> c3(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, add(z0, z1)))) A__ADD(s(add(x0, s(z0))), x2) -> c3(A__ADD(a__add(mark(x0), s(mark(z0))), mark(x2)), MARK(add(x0, s(z0)))) A__ADD(s(add(x0, 0)), x2) -> c3(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(add(x0, 0))) A__ADD(s(add(x0, true)), x2) -> c3(A__ADD(a__add(mark(x0), true), mark(x2)), MARK(add(x0, true))) A__ADD(s(add(x0, false)), x2) -> c3(A__ADD(a__add(mark(x0), false), mark(x2)), MARK(add(x0, false))) A__ADD(s(add(fact(z0), x1)), x2) -> c3(A__ADD(a__add(a__fact(mark(z0)), mark(x1)), mark(x2)), MARK(add(fact(z0), x1))) A__ADD(s(add(if(z0, z1, z2), x1)), x2) -> c3(A__ADD(a__add(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(add(if(z0, z1, z2), x1))) A__ADD(s(add(zero(z0), x1)), x2) -> c3(A__ADD(a__add(a__zero(mark(z0)), mark(x1)), mark(x2)), MARK(add(zero(z0), x1))) A__ADD(s(add(prod(z0, z1), x1)), x2) -> c3(A__ADD(a__add(a__prod(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(prod(z0, z1), x1))) A__ADD(s(add(p(z0), x1)), x2) -> c3(A__ADD(a__add(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(add(p(z0), x1))) A__ADD(s(add(add(z0, z1), x1)), x2) -> c3(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(add(z0, z1), x1))) A__ADD(s(add(s(z0), x1)), x2) -> c3(A__ADD(a__add(s(mark(z0)), mark(x1)), mark(x2)), MARK(add(s(z0), x1))) A__ADD(s(add(0, x1)), x2) -> c3(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(add(0, x1))) A__ADD(s(add(true, x1)), x2) -> c3(A__ADD(a__add(true, mark(x1)), mark(x2)), MARK(add(true, x1))) A__ADD(s(add(false, x1)), x2) -> c3(A__ADD(a__add(false, mark(x1)), mark(x2)), MARK(add(false, x1))) A__ADD(s(add(x0, x1)), x2) -> c3(MARK(add(x0, x1))) A__ADD(s(s(fact(z0))), x1) -> c3(A__ADD(s(a__fact(mark(z0))), mark(x1)), MARK(s(fact(z0)))) A__ADD(s(s(if(z0, z1, z2))), x1) -> c3(A__ADD(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(s(if(z0, z1, z2)))) A__ADD(s(s(zero(z0))), x1) -> c3(A__ADD(s(a__zero(mark(z0))), mark(x1)), MARK(s(zero(z0)))) A__ADD(s(s(prod(z0, z1))), x1) -> c3(A__ADD(s(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(s(prod(z0, z1)))) A__ADD(s(s(p(z0))), x1) -> c3(A__ADD(s(a__p(mark(z0))), mark(x1)), MARK(s(p(z0)))) A__ADD(s(s(add(z0, z1))), x1) -> c3(A__ADD(s(a__add(mark(z0), mark(z1))), mark(x1)), MARK(s(add(z0, z1)))) A__ADD(s(s(s(z0))), x1) -> c3(A__ADD(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__ADD(s(s(0)), x1) -> c3(A__ADD(s(0), mark(x1)), MARK(s(0))) A__ADD(s(s(true)), x1) -> c3(A__ADD(s(true), mark(x1)), MARK(s(true))) A__ADD(s(s(false)), x1) -> c3(A__ADD(s(false), mark(x1)), MARK(s(false))) A__ADD(s(s(x0)), x1) -> c3(MARK(s(x0))) A__ADD(s(x0), fact(x1)) -> c4(A__ADD(mark(x0), a__if(a__zero(mark(mark(x1))), s(0), prod(mark(x1), fact(p(mark(x1)))))), MARK(fact(x1))) A__ADD(s(x0), fact(x1)) -> c4(A__ADD(mark(x0), fact(mark(x1))), MARK(fact(x1))) A__ADD(s(x0), fact(fact(z0))) -> c4(A__ADD(mark(x0), a__fact(a__fact(mark(z0)))), MARK(fact(fact(z0)))) A__ADD(s(x0), fact(if(z0, z1, z2))) -> c4(A__ADD(mark(x0), a__fact(a__if(mark(z0), z1, z2))), MARK(fact(if(z0, z1, z2)))) A__ADD(s(x0), fact(zero(z0))) -> c4(A__ADD(mark(x0), a__fact(a__zero(mark(z0)))), MARK(fact(zero(z0)))) A__ADD(s(x0), fact(prod(z0, z1))) -> c4(A__ADD(mark(x0), a__fact(a__prod(mark(z0), mark(z1)))), MARK(fact(prod(z0, z1)))) A__ADD(s(x0), fact(p(z0))) -> c4(A__ADD(mark(x0), a__fact(a__p(mark(z0)))), MARK(fact(p(z0)))) A__ADD(s(x0), fact(add(z0, z1))) -> c4(A__ADD(mark(x0), a__fact(a__add(mark(z0), mark(z1)))), 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fact(x1)) -> c4(A__ADD(s(mark(z0)), a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(0), fact(x1)) -> c4(A__ADD(0, a__fact(mark(x1))), MARK(fact(x1))) A__ADD(s(x0), fact(x1)) -> c4(MARK(fact(x1))) A__ADD(s(true), fact(x1)) -> c4(MARK(fact(x1))) A__ADD(s(false), fact(x1)) -> c4(MARK(fact(x1))) A__ADD(s(x0), if(x1, z1, z2)) -> c4(A__ADD(mark(x0), if(mark(x1), z1, z2)), MARK(if(x1, z1, z2))) A__ADD(s(x0), if(fact(z0), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__fact(mark(z0)), x2, x3)), MARK(if(fact(z0), x2, x3))) A__ADD(s(x0), if(if(z0, z1, z2), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(if(if(z0, z1, z2), x2, x3))) A__ADD(s(x0), if(zero(z0), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__zero(mark(z0)), x2, x3)), MARK(if(zero(z0), x2, x3))) A__ADD(s(x0), if(prod(z0, z1), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__prod(mark(z0), mark(z1)), x2, x3)), MARK(if(prod(z0, z1), x2, x3))) A__ADD(s(x0), if(p(z0), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(if(p(z0), x2, x3))) A__ADD(s(x0), if(add(z0, z1), x2, x3)) -> c4(A__ADD(mark(x0), a__if(a__add(mark(z0), mark(z1)), x2, x3)), MARK(if(add(z0, z1), x2, x3))) A__ADD(s(x0), if(s(z0), x2, x3)) -> c4(A__ADD(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(if(s(z0), x2, x3))) A__ADD(s(x0), if(true, x2, x3)) -> c4(A__ADD(mark(x0), a__if(true, x2, x3)), MARK(if(true, x2, x3))) A__ADD(s(x0), if(false, x2, x3)) -> c4(A__ADD(mark(x0), a__if(false, x2, x3)), MARK(if(false, x2, x3))) A__ADD(s(fact(z0)), if(x1, x2, x3)) -> c4(A__ADD(a__fact(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(if(z0, z1, z2)), if(x1, x2, x3)) -> c4(A__ADD(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(zero(z0)), if(x1, x2, x3)) -> c4(A__ADD(a__zero(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(prod(z0, z1)), if(x1, x2, x3)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(p(z0)), if(x1, x2, x3)) -> c4(A__ADD(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(add(z0, z1)), if(x1, x2, x3)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(s(z0)), if(x1, x2, x3)) -> c4(A__ADD(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(0), if(x1, x2, x3)) -> c4(A__ADD(0, a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3))) A__ADD(s(x0), if(0, x2, x3)) -> c4(A__ADD(mark(x0), a__if(0, x2, x3))) A__ADD(s(true), if(x1, x2, x3)) -> c4(MARK(if(x1, x2, x3))) A__ADD(s(false), if(x1, x2, x3)) -> c4(MARK(if(x1, x2, x3))) A__ADD(s(x0), zero(x1)) -> c4(A__ADD(mark(x0), zero(mark(x1))), MARK(zero(x1))) A__ADD(s(x0), zero(fact(z0))) -> c4(A__ADD(mark(x0), a__zero(a__fact(mark(z0)))), MARK(zero(fact(z0)))) A__ADD(s(x0), zero(if(z0, z1, z2))) -> c4(A__ADD(mark(x0), a__zero(a__if(mark(z0), z1, z2))), MARK(zero(if(z0, z1, z2)))) A__ADD(s(x0), zero(zero(z0))) -> c4(A__ADD(mark(x0), a__zero(a__zero(mark(z0)))), MARK(zero(zero(z0)))) A__ADD(s(x0), zero(prod(z0, z1))) -> c4(A__ADD(mark(x0), a__zero(a__prod(mark(z0), mark(z1)))), MARK(zero(prod(z0, z1)))) A__ADD(s(x0), zero(p(z0))) -> c4(A__ADD(mark(x0), a__zero(a__p(mark(z0)))), MARK(zero(p(z0)))) A__ADD(s(x0), zero(add(z0, z1))) -> c4(A__ADD(mark(x0), a__zero(a__add(mark(z0), mark(z1)))), MARK(zero(add(z0, z1)))) A__ADD(s(x0), zero(s(z0))) -> c4(A__ADD(mark(x0), a__zero(s(mark(z0)))), MARK(zero(s(z0)))) A__ADD(s(x0), zero(0)) -> c4(A__ADD(mark(x0), a__zero(0)), MARK(zero(0))) A__ADD(s(x0), zero(true)) -> c4(A__ADD(mark(x0), a__zero(true)), MARK(zero(true))) A__ADD(s(x0), zero(false)) -> c4(A__ADD(mark(x0), a__zero(false)), MARK(zero(false))) A__ADD(s(fact(z0)), zero(x1)) -> c4(A__ADD(a__fact(mark(z0)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(if(z0, z1, z2)), zero(x1)) -> c4(A__ADD(a__if(mark(z0), z1, z2), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(zero(z0)), zero(x1)) -> c4(A__ADD(a__zero(mark(z0)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(prod(z0, z1)), zero(x1)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(p(z0)), zero(x1)) -> c4(A__ADD(a__p(mark(z0)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(add(z0, z1)), zero(x1)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(s(z0)), zero(x1)) -> c4(A__ADD(s(mark(z0)), a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(0), zero(x1)) -> c4(A__ADD(0, a__zero(mark(x1))), MARK(zero(x1))) A__ADD(s(x0), zero(x1)) -> c4(MARK(zero(x1))) A__ADD(s(true), zero(x1)) -> c4(MARK(zero(x1))) A__ADD(s(false), zero(x1)) -> c4(MARK(zero(x1))) A__ADD(s(x0), prod(x1, x2)) -> c4(A__ADD(mark(x0), prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(x0), prod(x1, fact(z0))) -> c4(A__ADD(mark(x0), a__prod(mark(x1), a__fact(mark(z0)))), MARK(prod(x1, fact(z0)))) A__ADD(s(x0), prod(x1, if(z0, z1, z2))) -> c4(A__ADD(mark(x0), a__prod(mark(x1), a__if(mark(z0), z1, z2))), MARK(prod(x1, if(z0, z1, z2)))) A__ADD(s(x0), prod(x1, zero(z0))) -> c4(A__ADD(mark(x0), a__prod(mark(x1), a__zero(mark(z0)))), MARK(prod(x1, zero(z0)))) A__ADD(s(x0), prod(x1, prod(z0, z1))) -> c4(A__ADD(mark(x0), a__prod(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(prod(x1, prod(z0, z1)))) A__ADD(s(x0), prod(x1, p(z0))) -> c4(A__ADD(mark(x0), a__prod(mark(x1), a__p(mark(z0)))), MARK(prod(x1, p(z0)))) A__ADD(s(x0), prod(x1, add(z0, z1))) -> c4(A__ADD(mark(x0), a__prod(mark(x1), a__add(mark(z0), mark(z1)))), MARK(prod(x1, add(z0, z1)))) A__ADD(s(x0), prod(x1, s(z0))) -> c4(A__ADD(mark(x0), a__prod(mark(x1), s(mark(z0)))), MARK(prod(x1, s(z0)))) A__ADD(s(x0), prod(x1, 0)) -> c4(A__ADD(mark(x0), a__prod(mark(x1), 0)), MARK(prod(x1, 0))) A__ADD(s(x0), prod(x1, true)) -> c4(A__ADD(mark(x0), a__prod(mark(x1), true)), MARK(prod(x1, true))) A__ADD(s(x0), prod(x1, false)) -> c4(A__ADD(mark(x0), a__prod(mark(x1), false)), MARK(prod(x1, false))) A__ADD(s(x0), prod(fact(z0), x2)) -> c4(A__ADD(mark(x0), a__prod(a__fact(mark(z0)), mark(x2))), MARK(prod(fact(z0), x2))) A__ADD(s(x0), prod(if(z0, z1, z2), x2)) -> c4(A__ADD(mark(x0), a__prod(a__if(mark(z0), z1, z2), mark(x2))), MARK(prod(if(z0, z1, z2), x2))) A__ADD(s(x0), prod(zero(z0), x2)) -> c4(A__ADD(mark(x0), a__prod(a__zero(mark(z0)), mark(x2))), MARK(prod(zero(z0), x2))) A__ADD(s(x0), prod(prod(z0, z1), x2)) -> c4(A__ADD(mark(x0), a__prod(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(prod(prod(z0, z1), x2))) A__ADD(s(x0), prod(p(z0), x2)) -> c4(A__ADD(mark(x0), a__prod(a__p(mark(z0)), mark(x2))), MARK(prod(p(z0), x2))) A__ADD(s(x0), prod(add(z0, z1), x2)) -> c4(A__ADD(mark(x0), a__prod(a__add(mark(z0), mark(z1)), mark(x2))), MARK(prod(add(z0, z1), x2))) A__ADD(s(x0), prod(s(z0), x2)) -> c4(A__ADD(mark(x0), a__prod(s(mark(z0)), mark(x2))), MARK(prod(s(z0), x2))) A__ADD(s(x0), prod(0, x2)) -> c4(A__ADD(mark(x0), a__prod(0, mark(x2))), MARK(prod(0, x2))) A__ADD(s(x0), prod(true, x2)) -> c4(A__ADD(mark(x0), a__prod(true, mark(x2))), MARK(prod(true, x2))) A__ADD(s(x0), prod(false, x2)) -> c4(A__ADD(mark(x0), a__prod(false, mark(x2))), MARK(prod(false, x2))) A__ADD(s(fact(z0)), prod(x1, x2)) -> c4(A__ADD(a__fact(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(if(z0, z1, z2)), prod(x1, x2)) -> c4(A__ADD(a__if(mark(z0), z1, z2), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(zero(z0)), prod(x1, x2)) -> c4(A__ADD(a__zero(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(prod(z0, z1)), prod(x1, x2)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(p(z0)), prod(x1, x2)) -> c4(A__ADD(a__p(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(add(z0, z1)), prod(x1, x2)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(s(z0)), prod(x1, x2)) -> c4(A__ADD(s(mark(z0)), a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(0), prod(x1, x2)) -> c4(A__ADD(0, a__prod(mark(x1), mark(x2))), MARK(prod(x1, x2))) A__ADD(s(true), prod(x1, x2)) -> c4(MARK(prod(x1, x2))) A__ADD(s(false), prod(x1, x2)) -> c4(MARK(prod(x1, x2))) A__ADD(s(x0), p(x1)) -> c4(A__ADD(mark(x0), p(mark(x1))), MARK(p(x1))) A__ADD(s(x0), p(fact(z0))) -> c4(A__ADD(mark(x0), a__p(a__fact(mark(z0)))), MARK(p(fact(z0)))) A__ADD(s(x0), p(if(z0, z1, z2))) -> c4(A__ADD(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(p(if(z0, z1, z2)))) A__ADD(s(x0), p(zero(z0))) -> c4(A__ADD(mark(x0), a__p(a__zero(mark(z0)))), MARK(p(zero(z0)))) A__ADD(s(x0), p(prod(z0, z1))) -> c4(A__ADD(mark(x0), a__p(a__prod(mark(z0), mark(z1)))), MARK(p(prod(z0, z1)))) A__ADD(s(x0), p(p(z0))) -> c4(A__ADD(mark(x0), a__p(a__p(mark(z0)))), MARK(p(p(z0)))) A__ADD(s(x0), p(add(z0, z1))) -> c4(A__ADD(mark(x0), a__p(a__add(mark(z0), mark(z1)))), MARK(p(add(z0, z1)))) A__ADD(s(x0), p(s(z0))) -> c4(A__ADD(mark(x0), a__p(s(mark(z0)))), MARK(p(s(z0)))) A__ADD(s(fact(z0)), p(x1)) -> c4(A__ADD(a__fact(mark(z0)), a__p(mark(x1))), MARK(p(x1))) A__ADD(s(if(z0, z1, z2)), p(x1)) -> c4(A__ADD(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(p(x1))) A__ADD(s(zero(z0)), p(x1)) -> c4(A__ADD(a__zero(mark(z0)), a__p(mark(x1))), MARK(p(x1))) A__ADD(s(prod(z0, z1)), p(x1)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), a__p(mark(x1))), MARK(p(x1))) A__ADD(s(p(z0)), p(x1)) -> c4(A__ADD(a__p(mark(z0)), a__p(mark(x1))), MARK(p(x1))) A__ADD(s(add(z0, z1)), p(x1)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), a__p(mark(x1))), MARK(p(x1))) A__ADD(s(s(z0)), p(x1)) -> c4(A__ADD(s(mark(z0)), a__p(mark(x1))), MARK(p(x1))) A__ADD(s(0), p(x1)) -> c4(A__ADD(0, a__p(mark(x1))), MARK(p(x1))) A__ADD(s(x0), p(0)) -> c4(A__ADD(mark(x0), a__p(0))) A__ADD(s(x0), p(true)) -> c4(A__ADD(mark(x0), a__p(true))) A__ADD(s(x0), p(false)) -> c4(A__ADD(mark(x0), a__p(false))) A__ADD(s(true), p(x1)) -> c4(MARK(p(x1))) A__ADD(s(false), p(x1)) -> c4(MARK(p(x1))) A__ADD(s(x0), add(x1, x2)) -> c4(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(add(x1, x2))) A__ADD(s(x0), add(x1, fact(z0))) -> c4(A__ADD(mark(x0), a__add(mark(x1), a__fact(mark(z0)))), MARK(add(x1, fact(z0)))) A__ADD(s(x0), add(x1, if(z0, z1, z2))) -> c4(A__ADD(mark(x0), a__add(mark(x1), a__if(mark(z0), z1, z2))), MARK(add(x1, if(z0, z1, z2)))) A__ADD(s(x0), add(x1, zero(z0))) -> c4(A__ADD(mark(x0), a__add(mark(x1), a__zero(mark(z0)))), MARK(add(x1, zero(z0)))) A__ADD(s(x0), add(x1, prod(z0, z1))) -> c4(A__ADD(mark(x0), a__add(mark(x1), a__prod(mark(z0), mark(z1)))), MARK(add(x1, prod(z0, z1)))) A__ADD(s(x0), add(x1, p(z0))) -> c4(A__ADD(mark(x0), a__add(mark(x1), a__p(mark(z0)))), MARK(add(x1, p(z0)))) A__ADD(s(x0), add(x1, add(z0, z1))) -> c4(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(add(x1, add(z0, z1)))) A__ADD(s(x0), add(x1, s(z0))) -> c4(A__ADD(mark(x0), a__add(mark(x1), s(mark(z0)))), MARK(add(x1, s(z0)))) A__ADD(s(x0), add(x1, 0)) -> c4(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(add(x1, 0))) A__ADD(s(x0), add(x1, true)) -> c4(A__ADD(mark(x0), a__add(mark(x1), true)), MARK(add(x1, true))) A__ADD(s(x0), add(x1, false)) -> c4(A__ADD(mark(x0), a__add(mark(x1), false)), MARK(add(x1, false))) A__ADD(s(x0), add(fact(z0), x2)) -> c4(A__ADD(mark(x0), a__add(a__fact(mark(z0)), mark(x2))), MARK(add(fact(z0), x2))) A__ADD(s(x0), add(if(z0, z1, z2), x2)) -> c4(A__ADD(mark(x0), a__add(a__if(mark(z0), z1, z2), mark(x2))), MARK(add(if(z0, z1, z2), x2))) A__ADD(s(x0), add(zero(z0), x2)) -> c4(A__ADD(mark(x0), a__add(a__zero(mark(z0)), mark(x2))), MARK(add(zero(z0), x2))) A__ADD(s(x0), add(prod(z0, z1), x2)) -> c4(A__ADD(mark(x0), a__add(a__prod(mark(z0), mark(z1)), mark(x2))), MARK(add(prod(z0, z1), x2))) A__ADD(s(x0), add(p(z0), x2)) -> c4(A__ADD(mark(x0), a__add(a__p(mark(z0)), mark(x2))), MARK(add(p(z0), x2))) A__ADD(s(x0), add(add(z0, z1), x2)) -> c4(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(add(add(z0, z1), x2))) A__ADD(s(x0), add(s(z0), x2)) -> c4(A__ADD(mark(x0), a__add(s(mark(z0)), mark(x2))), MARK(add(s(z0), x2))) A__ADD(s(x0), add(0, x2)) -> c4(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(add(0, x2))) A__ADD(s(x0), add(true, x2)) -> c4(A__ADD(mark(x0), a__add(true, mark(x2))), MARK(add(true, x2))) A__ADD(s(x0), add(false, x2)) -> c4(A__ADD(mark(x0), a__add(false, mark(x2))), MARK(add(false, x2))) A__ADD(s(fact(z0)), add(x1, x2)) -> c4(A__ADD(a__fact(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) A__ADD(s(if(z0, z1, z2)), add(x1, x2)) -> c4(A__ADD(a__if(mark(z0), z1, z2), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) A__ADD(s(zero(z0)), add(x1, x2)) -> c4(A__ADD(a__zero(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) A__ADD(s(prod(z0, z1)), add(x1, x2)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) A__ADD(s(p(z0)), add(x1, x2)) -> c4(A__ADD(a__p(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) A__ADD(s(add(z0, z1)), add(x1, x2)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) A__ADD(s(s(z0)), add(x1, x2)) -> c4(A__ADD(s(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) A__ADD(s(0), add(x1, x2)) -> c4(A__ADD(0, a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) A__ADD(s(true), add(x1, x2)) -> c4(MARK(add(x1, x2))) A__ADD(s(false), add(x1, x2)) -> c4(MARK(add(x1, x2))) K tuples:none Defined Rule Symbols: a__fact_1, a__add_2, a__prod_2, a__if_3, a__zero_1, a__p_1, mark_1 Defined Pair Symbols: A__ADD_2, A__IF_3, A__P_1, MARK_1, A__PROD_2, A__FACT_1 Compound Symbols: c2_1, c11_1, c12_1, c17_1, c19_2, c27_1, c21_1, c3_1, c4_2, c4_1, c7_2, c7_1, c8_3, c8_2, c9_3, c9_2, c9_1, c20_2, c20_1, c22_2, c23_2, c23_1, c24_2, c25_2, c25_1, c26_2, c26_1, c_2, c_1, c3_2