KILLED proof of input_nbe1p8WQpN.trs # AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). (0) CpxTRS (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxTRS (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (4) CpxTRS (5) RelTrsToWeightedTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxWeightedTrs (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxTypedWeightedTrs (9) CompletionProof [UPPER BOUND(ID), 0 ms] (10) CpxTypedWeightedCompleteTrs (11) NarrowingProof [BOTH BOUNDS(ID, ID), 399 ms] (12) CpxTypedWeightedCompleteTrs (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (14) CpxRNTS (15) InliningProof [UPPER BOUND(ID), 441 ms] (16) CpxRNTS (17) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (18) CpxRNTS (19) CompletionProof [UPPER BOUND(ID), 0 ms] (20) CpxTypedWeightedCompleteTrs (21) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (22) CpxRNTS (23) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (24) CdtProblem (25) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (26) CdtProblem (27) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (28) CdtProblem (29) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 4 ms] (30) CdtProblem (31) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (32) CdtProblem (33) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (34) CdtProblem (35) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1 ms] (36) CdtProblem (37) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (38) CdtProblem (39) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (40) CdtProblem (41) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (42) CdtProblem (43) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (44) CdtProblem (45) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 30 ms] (46) CdtProblem (47) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (48) CdtProblem (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 35 ms] (50) CdtProblem (51) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 13 ms] (52) CdtProblem (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (54) CdtProblem (55) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (56) CdtProblem (57) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (58) CdtProblem (59) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 3 ms] (60) CdtProblem (61) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (62) CdtProblem (63) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 52 ms] (64) CdtProblem (65) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (66) CdtProblem (67) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 16 ms] (68) CdtProblem (69) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (70) CdtProblem (71) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 39 ms] (72) CdtProblem (73) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 13 ms] (74) CdtProblem (75) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (76) CdtProblem (77) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 50 ms] (78) CdtProblem (79) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (80) CdtProblem (81) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (82) CdtProblem (83) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (84) CdtProblem (85) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 86 ms] (86) CdtProblem (87) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (88) CdtProblem (89) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 11 ms] (90) CdtProblem (91) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 134 ms] (92) CdtProblem (93) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 26 ms] (94) CdtProblem (95) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (96) CdtProblem (97) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 94 ms] (98) CdtProblem (99) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (100) CdtProblem (101) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (102) CdtProblem (103) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 163 ms] (104) CdtProblem (105) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 19 ms] (106) CdtProblem (107) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (108) CdtProblem (109) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 114 ms] (110) CdtProblem (111) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (112) CdtProblem (113) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 19 ms] (114) CdtProblem (115) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 217 ms] (116) CdtProblem (117) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 3 ms] (118) CdtProblem (119) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 39 ms] (120) CdtProblem (121) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 125 ms] (122) CdtProblem (123) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 13 ms] (124) CdtProblem (125) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (126) CdtProblem (127) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 48 ms] (128) CdtProblem (129) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (130) CdtProblem (131) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 5 ms] (132) CdtProblem (133) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 62 ms] (134) CdtProblem (135) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 48 ms] (136) CdtProblem (137) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 38 ms] (138) CdtProblem (139) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 96 ms] (140) CdtProblem (141) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (142) CdtProblem (143) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 47 ms] (144) CdtProblem (145) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 179 ms] (146) CdtProblem (147) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (148) CdtProblem (149) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 190 ms] (150) CdtProblem (151) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 13 ms] (152) CdtProblem (153) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 244 ms] (154) CdtProblem (155) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 39 ms] (156) CdtProblem (157) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 331 ms] (158) CdtProblem (159) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 48 ms] (160) CdtProblem (161) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 262 ms] (162) CdtProblem (163) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 53 ms] (164) CdtProblem (165) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 462 ms] (166) CdtProblem (167) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 46 ms] (168) CdtProblem (169) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 292 ms] (170) CdtProblem (171) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 286 ms] (172) CdtProblem (173) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 79 ms] (174) CdtProblem (175) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 332 ms] (176) CdtProblem (177) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 79 ms] (178) CdtProblem (179) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 395 ms] (180) CdtProblem (181) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 86 ms] (182) CdtProblem (183) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 505 ms] (184) CdtProblem (185) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 71 ms] (186) CdtProblem (187) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 356 ms] (188) CdtProblem (189) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 109 ms] (190) CdtProblem (191) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 553 ms] (192) CdtProblem (193) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 91 ms] (194) CdtProblem (195) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 359 ms] (196) CdtProblem (197) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 139 ms] (198) CdtProblem (199) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 458 ms] (200) CdtProblem (201) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 136 ms] (202) CdtProblem (203) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 533 ms] (204) 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) RelTrsToWeightedTrsProof (UPPER BOUND(ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (6) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: a__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 ---------------------------------------- (7) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (8) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__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 ---------------------------------------- (9) CompletionProof (UPPER BOUND(ID)) The transformation into a RNTS is sound, since: (a) The obligation is a constructor system where every type has a constant constructor, (b) The following defined symbols do not have to be completely defined, as they can never occur inside other defined symbols: none (c) The following functions are completely defined: 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 ---------------------------------------- (10) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__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 ---------------------------------------- (11) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (12) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__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 ---------------------------------------- (13) 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 ---------------------------------------- (14) 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 ---------------------------------------- (15) 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 ---------------------------------------- (16) 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 ---------------------------------------- (17) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (18) 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 ---------------------------------------- (19) 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 ---------------------------------------- (20) 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 ---------------------------------------- (21) 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 ---------------------------------------- (22) 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. ---------------------------------------- (23) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT ---------------------------------------- (24) 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 ---------------------------------------- (25) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 12 trailing nodes: A__PROD(z0, z1) -> c10 MARK(true) -> c29 A__FACT(z0) -> c1 MARK(0) -> c28 A__ZERO(z0) -> c16 MARK(false) -> c30 A__PROD(0, z0) -> c6 A__ZERO(s(z0)) -> c15 A__ADD(z0, z1) -> c5 A__P(z0) -> c18 A__ZERO(0) -> c14 A__IF(z0, z1, z2) -> c13 ---------------------------------------- (26) 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 ---------------------------------------- (27) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (28) 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 ---------------------------------------- (29) 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)) ---------------------------------------- (30) 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 ---------------------------------------- (31) 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)) ---------------------------------------- (32) 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 ---------------------------------------- (33) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (34) 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 ---------------------------------------- (35) 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)) ---------------------------------------- (36) 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 ---------------------------------------- (37) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing tuple parts ---------------------------------------- (38) 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 ---------------------------------------- (39) 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)) ---------------------------------------- (40) 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 ---------------------------------------- (41) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: 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)) ---------------------------------------- (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__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 ---------------------------------------- (43) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (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__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 ---------------------------------------- (45) 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)) ---------------------------------------- (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__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 ---------------------------------------- (47) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing tuple parts ---------------------------------------- (48) 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 ---------------------------------------- (49) 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)) ---------------------------------------- (50) 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 ---------------------------------------- (51) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 8 trailing tuple parts ---------------------------------------- (52) 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 ---------------------------------------- (53) 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)) ---------------------------------------- (54) 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 ---------------------------------------- (55) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(if(0, x1, x2)) -> c20(A__IF(0, x1, x2), MARK(0)) ---------------------------------------- (56) 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 ---------------------------------------- (57) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (58) 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 ---------------------------------------- (59) 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)) ---------------------------------------- (60) 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 ---------------------------------------- (61) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing nodes: MARK(prod(0, x1)) -> c22(A__PROD(0, mark(x1)), MARK(0)) MARK(prod(false, x1)) -> c22(A__PROD(false, mark(x1)), MARK(false)) MARK(prod(true, x1)) -> c22(A__PROD(true, mark(x1)), MARK(true)) ---------------------------------------- (62) 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 ---------------------------------------- (63) 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)) ---------------------------------------- (64) 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 ---------------------------------------- (65) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 6 trailing tuple parts ---------------------------------------- (66) 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 ---------------------------------------- (67) 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)) ---------------------------------------- (68) 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 ---------------------------------------- (69) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing nodes: MARK(p(false)) -> c24(A__P(false), MARK(false)) MARK(p(true)) -> c24(A__P(true), MARK(true)) MARK(p(0)) -> c24(A__P(0), MARK(0)) ---------------------------------------- (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__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 ---------------------------------------- (71) 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)) ---------------------------------------- (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__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 ---------------------------------------- (73) 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)) ---------------------------------------- (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__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 ---------------------------------------- (75) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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__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 ---------------------------------------- (77) 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)) ---------------------------------------- (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__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), 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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 ---------------------------------------- (79) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing tuple parts ---------------------------------------- (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__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 ---------------------------------------- (81) 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)) ---------------------------------------- (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__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 ---------------------------------------- (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__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 ---------------------------------------- (85) 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)) ---------------------------------------- (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__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 ---------------------------------------- (87) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: 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)) ---------------------------------------- (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__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)) 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 ---------------------------------------- (89) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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(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 ---------------------------------------- (91) 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)) ---------------------------------------- (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(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)) 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 ---------------------------------------- (93) 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)) ---------------------------------------- (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(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 ---------------------------------------- (95) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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(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 ---------------------------------------- (97) 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)) ---------------------------------------- (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(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 ---------------------------------------- (99) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: A__ADD(s(false), zero(x1)) -> c3(A__ADD(false, a__zero(mark(x1))), MARK(false)) A__ADD(s(true), zero(x1)) -> c3(A__ADD(true, a__zero(mark(x1))), MARK(true)) ---------------------------------------- (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(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 ---------------------------------------- (101) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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(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)) 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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 ---------------------------------------- (103) 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)) ---------------------------------------- (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(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)) 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))) -> 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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 ---------------------------------------- (105) 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)) ---------------------------------------- (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(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 ---------------------------------------- (107) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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(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)))) 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 ---------------------------------------- (109) 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)) ---------------------------------------- (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(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), 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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)) -> 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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))), 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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 ---------------------------------------- (111) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: A__ADD(s(false), p(x1)) -> c3(A__ADD(false, a__p(mark(x1))), MARK(false)) A__ADD(s(true), p(x1)) -> c3(A__ADD(true, a__p(mark(x1))), MARK(true)) ---------------------------------------- (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(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)) 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)) 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 ---------------------------------------- (113) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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(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)) -> 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)))) 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 ---------------------------------------- (115) 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)) ---------------------------------------- (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(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), 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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))), 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, 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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))), 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 ---------------------------------------- (117) 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)) ---------------------------------------- (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)) 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)) 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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, 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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 ---------------------------------------- (119) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 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)) 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 ---------------------------------------- (121) 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)) ---------------------------------------- (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), 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)) 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)) -> 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)) 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 ---------------------------------------- (123) 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)) ---------------------------------------- (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), 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))), 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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)) 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) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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), 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))) -> 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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)))) 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), 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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)))) 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) 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)) ---------------------------------------- (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), 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)) 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 ---------------------------------------- (129) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: A__ADD(s(true), 0) -> c3(A__ADD(true, 0), MARK(true)) A__ADD(s(false), 0) -> c3(A__ADD(false, 0), MARK(false)) ---------------------------------------- (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), 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)) 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 ---------------------------------------- (131) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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), 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)))) 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 ---------------------------------------- (133) 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)) ---------------------------------------- (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), 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)), 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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(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)) 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, 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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)) -> 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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 ---------------------------------------- (135) 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)) ---------------------------------------- (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), 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)) 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)), 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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 ---------------------------------------- (137) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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), 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)) 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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)))) 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 ---------------------------------------- (139) 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)) ---------------------------------------- (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(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), 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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))) 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)), 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)) 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) 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)) ---------------------------------------- (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(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, 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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))) 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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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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 ---------------------------------------- (143) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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(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))), 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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))), 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)) 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) 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))) ---------------------------------------- (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(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))) -> 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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)) -> 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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))) 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(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), 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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(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))) 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)), 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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)) 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 ---------------------------------------- (149) 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))) ---------------------------------------- (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(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), 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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), 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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 ---------------------------------------- (151) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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(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 ---------------------------------------- (153) 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))) ---------------------------------------- (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(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), 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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), 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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(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))) -> 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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) -> 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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 ---------------------------------------- (155) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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(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))) 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)) -> 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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 ---------------------------------------- (157) 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))) ---------------------------------------- (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(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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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, 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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)), 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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))) 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(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))) -> 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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), 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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), 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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), 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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__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))) 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)) -> 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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))) 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(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))) ---------------------------------------- (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(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)) 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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))) 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) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (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(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, 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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, 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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), 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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)), 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))), 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, 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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, 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 ---------------------------------------- (165) 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))) ---------------------------------------- (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(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), 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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), 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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)), 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, 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, 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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)), 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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)), 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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, 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 ---------------------------------------- (167) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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(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), 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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))) 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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, 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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)) -> 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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))) 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) 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))) ---------------------------------------- (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(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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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), 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)), 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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))) 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 ---------------------------------------- (171) 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))) ---------------------------------------- (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(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)) -> 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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))), 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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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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), 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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(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 ---------------------------------------- (173) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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(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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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))) 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)) -> 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), 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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))) 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 ---------------------------------------- (175) 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))) ---------------------------------------- (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(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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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, 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), 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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))) 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 ---------------------------------------- (177) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 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(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))) -> 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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))) 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, 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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) 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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))) 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 ---------------------------------------- (179) 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))) ---------------------------------------- (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(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) -> 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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))) 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)), 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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(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 ---------------------------------------- (181) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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(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)), 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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))) -> 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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), 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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)) 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) -> 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-> 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 ---------------------------------------- (183) 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))) ---------------------------------------- (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(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), 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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))) 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, 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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))), 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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(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 ---------------------------------------- (185) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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(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)), 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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(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) -> 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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))) 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)) 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), 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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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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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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(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 ---------------------------------------- (187) 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))) ---------------------------------------- (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(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 ---------------------------------------- (189) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing tuple parts ---------------------------------------- (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(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 ---------------------------------------- (191) 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))) ---------------------------------------- (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(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 ---------------------------------------- (193) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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(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 ---------------------------------------- (195) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__ADD(s(x0), s(z0)) -> c4(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) by A__ADD(s(x0), s(fact(z0))) -> c4(A__ADD(mark(x0), s(a__fact(mark(z0)))), MARK(s(fact(z0)))) A__ADD(s(x0), s(if(z0, z1, z2))) -> c4(A__ADD(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(s(if(z0, z1, z2)))) A__ADD(s(x0), s(zero(z0))) -> c4(A__ADD(mark(x0), s(a__zero(mark(z0)))), MARK(s(zero(z0)))) A__ADD(s(x0), s(prod(z0, z1))) -> c4(A__ADD(mark(x0), s(a__prod(mark(z0), mark(z1)))), MARK(s(prod(z0, z1)))) A__ADD(s(x0), s(p(z0))) -> c4(A__ADD(mark(x0), s(a__p(mark(z0)))), MARK(s(p(z0)))) A__ADD(s(x0), s(add(z0, z1))) -> c4(A__ADD(mark(x0), s(a__add(mark(z0), mark(z1)))), MARK(s(add(z0, z1)))) A__ADD(s(x0), s(s(z0))) -> c4(A__ADD(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__ADD(s(x0), s(0)) -> c4(A__ADD(mark(x0), s(0)), MARK(s(0))) A__ADD(s(x0), s(true)) -> c4(A__ADD(mark(x0), s(true)), MARK(s(true))) A__ADD(s(x0), s(false)) -> c4(A__ADD(mark(x0), s(false)), MARK(s(false))) A__ADD(s(fact(z0)), s(x1)) -> c4(A__ADD(a__fact(mark(z0)), s(mark(x1))), MARK(s(x1))) A__ADD(s(if(z0, z1, z2)), s(x1)) -> c4(A__ADD(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(s(x1))) A__ADD(s(zero(z0)), s(x1)) -> c4(A__ADD(a__zero(mark(z0)), s(mark(x1))), MARK(s(x1))) A__ADD(s(prod(z0, z1)), s(x1)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__ADD(s(p(z0)), s(x1)) -> c4(A__ADD(a__p(mark(z0)), s(mark(x1))), MARK(s(x1))) A__ADD(s(add(z0, z1)), s(x1)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__ADD(s(s(z0)), s(x1)) -> c4(A__ADD(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__ADD(s(0), s(x1)) -> c4(A__ADD(0, s(mark(x1))), MARK(s(x1))) A__ADD(s(true), s(x1)) -> c4(A__ADD(true, s(mark(x1))), MARK(s(x1))) A__ADD(s(false), s(x1)) -> c4(A__ADD(false, s(mark(x1))), MARK(s(x1))) A__ADD(s(x0), s(x1)) -> c4(MARK(s(x1))) ---------------------------------------- (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(0), x1) -> c3(A__ADD(0, mark(x1))) 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))) 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))) 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))) A__ADD(s(x0), s(fact(z0))) -> c4(A__ADD(mark(x0), s(a__fact(mark(z0)))), MARK(s(fact(z0)))) A__ADD(s(x0), s(if(z0, z1, z2))) -> c4(A__ADD(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(s(if(z0, z1, z2)))) A__ADD(s(x0), s(zero(z0))) -> c4(A__ADD(mark(x0), s(a__zero(mark(z0)))), MARK(s(zero(z0)))) A__ADD(s(x0), s(prod(z0, z1))) -> c4(A__ADD(mark(x0), s(a__prod(mark(z0), mark(z1)))), MARK(s(prod(z0, z1)))) A__ADD(s(x0), s(p(z0))) -> c4(A__ADD(mark(x0), s(a__p(mark(z0)))), MARK(s(p(z0)))) A__ADD(s(x0), s(add(z0, z1))) -> c4(A__ADD(mark(x0), s(a__add(mark(z0), mark(z1)))), MARK(s(add(z0, z1)))) A__ADD(s(x0), s(s(z0))) -> c4(A__ADD(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__ADD(s(x0), s(0)) -> c4(A__ADD(mark(x0), s(0)), MARK(s(0))) A__ADD(s(x0), s(true)) -> c4(A__ADD(mark(x0), s(true)), MARK(s(true))) A__ADD(s(x0), s(false)) -> c4(A__ADD(mark(x0), s(false)), MARK(s(false))) A__ADD(s(fact(z0)), s(x1)) -> c4(A__ADD(a__fact(mark(z0)), s(mark(x1))), MARK(s(x1))) A__ADD(s(if(z0, z1, z2)), s(x1)) -> c4(A__ADD(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(s(x1))) A__ADD(s(zero(z0)), s(x1)) -> c4(A__ADD(a__zero(mark(z0)), s(mark(x1))), MARK(s(x1))) A__ADD(s(prod(z0, z1)), s(x1)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__ADD(s(p(z0)), s(x1)) -> c4(A__ADD(a__p(mark(z0)), s(mark(x1))), MARK(s(x1))) A__ADD(s(add(z0, z1)), s(x1)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__ADD(s(s(z0)), s(x1)) -> c4(A__ADD(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__ADD(s(0), s(x1)) -> c4(A__ADD(0, s(mark(x1))), MARK(s(x1))) A__ADD(s(true), s(x1)) -> c4(A__ADD(true, s(mark(x1))), MARK(s(x1))) A__ADD(s(false), s(x1)) -> c4(A__ADD(false, s(mark(x1))), MARK(s(x1))) A__ADD(s(x0), s(x1)) -> c4(MARK(s(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(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), 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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))) 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))) A__ADD(s(x0), s(fact(z0))) -> c4(A__ADD(mark(x0), s(a__fact(mark(z0)))), MARK(s(fact(z0)))) A__ADD(s(x0), s(if(z0, z1, z2))) -> c4(A__ADD(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(s(if(z0, z1, z2)))) A__ADD(s(x0), s(zero(z0))) -> c4(A__ADD(mark(x0), s(a__zero(mark(z0)))), MARK(s(zero(z0)))) A__ADD(s(x0), s(prod(z0, z1))) -> c4(A__ADD(mark(x0), s(a__prod(mark(z0), mark(z1)))), MARK(s(prod(z0, z1)))) A__ADD(s(x0), s(p(z0))) -> c4(A__ADD(mark(x0), s(a__p(mark(z0)))), MARK(s(p(z0)))) A__ADD(s(x0), s(add(z0, z1))) -> c4(A__ADD(mark(x0), s(a__add(mark(z0), mark(z1)))), MARK(s(add(z0, z1)))) A__ADD(s(x0), s(s(z0))) -> c4(A__ADD(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__ADD(s(x0), s(0)) -> c4(A__ADD(mark(x0), s(0)), MARK(s(0))) A__ADD(s(x0), s(true)) -> c4(A__ADD(mark(x0), s(true)), MARK(s(true))) A__ADD(s(x0), s(false)) -> c4(A__ADD(mark(x0), s(false)), MARK(s(false))) A__ADD(s(fact(z0)), s(x1)) -> c4(A__ADD(a__fact(mark(z0)), s(mark(x1))), MARK(s(x1))) A__ADD(s(if(z0, z1, z2)), s(x1)) -> c4(A__ADD(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(s(x1))) A__ADD(s(zero(z0)), s(x1)) -> c4(A__ADD(a__zero(mark(z0)), s(mark(x1))), MARK(s(x1))) A__ADD(s(prod(z0, z1)), s(x1)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__ADD(s(p(z0)), s(x1)) -> c4(A__ADD(a__p(mark(z0)), s(mark(x1))), MARK(s(x1))) A__ADD(s(add(z0, z1)), s(x1)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__ADD(s(s(z0)), s(x1)) -> c4(A__ADD(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__ADD(s(0), s(x1)) -> c4(A__ADD(0, s(mark(x1))), MARK(s(x1))) A__ADD(s(true), s(x1)) -> c4(A__ADD(true, s(mark(x1))), MARK(s(x1))) A__ADD(s(false), s(x1)) -> c4(A__ADD(false, s(mark(x1))), MARK(s(x1))) A__ADD(s(x0), s(x1)) -> c4(MARK(s(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 ---------------------------------------- (197) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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(0), x1) -> c3(A__ADD(0, mark(x1))) 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__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), 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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))) A__ADD(s(x0), s(fact(z0))) -> c4(A__ADD(mark(x0), s(a__fact(mark(z0)))), MARK(s(fact(z0)))) A__ADD(s(x0), s(if(z0, z1, z2))) -> c4(A__ADD(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(s(if(z0, z1, z2)))) A__ADD(s(x0), s(zero(z0))) -> c4(A__ADD(mark(x0), s(a__zero(mark(z0)))), MARK(s(zero(z0)))) A__ADD(s(x0), s(prod(z0, z1))) -> c4(A__ADD(mark(x0), s(a__prod(mark(z0), mark(z1)))), MARK(s(prod(z0, z1)))) A__ADD(s(x0), s(p(z0))) -> c4(A__ADD(mark(x0), s(a__p(mark(z0)))), MARK(s(p(z0)))) A__ADD(s(x0), s(add(z0, z1))) -> c4(A__ADD(mark(x0), s(a__add(mark(z0), mark(z1)))), MARK(s(add(z0, z1)))) A__ADD(s(x0), s(s(z0))) -> c4(A__ADD(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__ADD(s(x0), s(0)) -> c4(A__ADD(mark(x0), s(0)), MARK(s(0))) A__ADD(s(x0), s(true)) -> c4(A__ADD(mark(x0), s(true)), MARK(s(true))) A__ADD(s(x0), s(false)) -> c4(A__ADD(mark(x0), s(false)), MARK(s(false))) A__ADD(s(fact(z0)), s(x1)) -> c4(A__ADD(a__fact(mark(z0)), s(mark(x1))), MARK(s(x1))) A__ADD(s(if(z0, z1, z2)), s(x1)) -> c4(A__ADD(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(s(x1))) A__ADD(s(zero(z0)), s(x1)) -> c4(A__ADD(a__zero(mark(z0)), s(mark(x1))), MARK(s(x1))) A__ADD(s(prod(z0, z1)), s(x1)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__ADD(s(p(z0)), s(x1)) -> c4(A__ADD(a__p(mark(z0)), s(mark(x1))), MARK(s(x1))) A__ADD(s(add(z0, z1)), s(x1)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__ADD(s(s(z0)), s(x1)) -> c4(A__ADD(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__ADD(s(0), s(x1)) -> c4(A__ADD(0, s(mark(x1))), MARK(s(x1))) A__ADD(s(x0), s(x1)) -> c4(MARK(s(x1))) A__ADD(s(true), s(x1)) -> c4(MARK(s(x1))) A__ADD(s(false), s(x1)) -> c4(MARK(s(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(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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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))) A__ADD(s(x0), s(fact(z0))) -> c4(A__ADD(mark(x0), s(a__fact(mark(z0)))), MARK(s(fact(z0)))) A__ADD(s(x0), s(if(z0, z1, z2))) -> c4(A__ADD(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(s(if(z0, z1, z2)))) A__ADD(s(x0), s(zero(z0))) -> c4(A__ADD(mark(x0), s(a__zero(mark(z0)))), MARK(s(zero(z0)))) A__ADD(s(x0), s(prod(z0, z1))) -> c4(A__ADD(mark(x0), s(a__prod(mark(z0), mark(z1)))), MARK(s(prod(z0, z1)))) A__ADD(s(x0), s(p(z0))) -> c4(A__ADD(mark(x0), s(a__p(mark(z0)))), MARK(s(p(z0)))) A__ADD(s(x0), s(add(z0, z1))) -> c4(A__ADD(mark(x0), s(a__add(mark(z0), mark(z1)))), MARK(s(add(z0, z1)))) A__ADD(s(x0), s(s(z0))) -> c4(A__ADD(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__ADD(s(x0), s(0)) -> c4(A__ADD(mark(x0), s(0)), MARK(s(0))) A__ADD(s(x0), s(true)) -> c4(A__ADD(mark(x0), s(true)), MARK(s(true))) A__ADD(s(x0), s(false)) -> c4(A__ADD(mark(x0), s(false)), MARK(s(false))) A__ADD(s(fact(z0)), s(x1)) -> c4(A__ADD(a__fact(mark(z0)), s(mark(x1))), MARK(s(x1))) A__ADD(s(if(z0, z1, z2)), s(x1)) -> c4(A__ADD(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(s(x1))) A__ADD(s(zero(z0)), s(x1)) -> c4(A__ADD(a__zero(mark(z0)), s(mark(x1))), MARK(s(x1))) A__ADD(s(prod(z0, z1)), s(x1)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__ADD(s(p(z0)), s(x1)) -> c4(A__ADD(a__p(mark(z0)), s(mark(x1))), MARK(s(x1))) A__ADD(s(add(z0, z1)), s(x1)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__ADD(s(s(z0)), s(x1)) -> c4(A__ADD(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__ADD(s(0), s(x1)) -> c4(A__ADD(0, s(mark(x1))), MARK(s(x1))) A__ADD(s(x0), s(x1)) -> c4(MARK(s(x1))) A__ADD(s(true), s(x1)) -> c4(MARK(s(x1))) A__ADD(s(false), s(x1)) -> c4(MARK(s(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 ---------------------------------------- (199) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__ADD(s(fact(z0)), x1) -> c4(A__ADD(a__fact(mark(z0)), mark(x1)), MARK(x1)) by A__ADD(s(fact(x0)), fact(z0)) -> c4(A__ADD(a__fact(mark(x0)), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(fact(x0)), if(z0, z1, z2)) -> c4(A__ADD(a__fact(mark(x0)), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(fact(x0)), zero(z0)) -> c4(A__ADD(a__fact(mark(x0)), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(fact(x0)), prod(z0, z1)) -> c4(A__ADD(a__fact(mark(x0)), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(fact(x0)), p(z0)) -> c4(A__ADD(a__fact(mark(x0)), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(fact(x0)), add(z0, z1)) -> c4(A__ADD(a__fact(mark(x0)), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(fact(x0)), s(z0)) -> c4(A__ADD(a__fact(mark(x0)), s(mark(z0))), MARK(s(z0))) A__ADD(s(fact(x0)), 0) -> c4(A__ADD(a__fact(mark(x0)), 0), MARK(0)) A__ADD(s(fact(x0)), true) -> c4(A__ADD(a__fact(mark(x0)), true), MARK(true)) A__ADD(s(fact(x0)), false) -> c4(A__ADD(a__fact(mark(x0)), false), MARK(false)) A__ADD(s(fact(x0)), x1) -> c4(A__ADD(a__if(a__zero(mark(mark(x0))), s(0), prod(mark(x0), fact(p(mark(x0))))), mark(x1)), MARK(x1)) A__ADD(s(fact(x0)), x1) -> c4(A__ADD(fact(mark(x0)), mark(x1)), MARK(x1)) A__ADD(s(fact(fact(z0))), x1) -> c4(A__ADD(a__fact(a__fact(mark(z0))), mark(x1)), MARK(x1)) A__ADD(s(fact(if(z0, z1, z2))), x1) -> c4(A__ADD(a__fact(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__ADD(s(fact(zero(z0))), x1) -> c4(A__ADD(a__fact(a__zero(mark(z0))), mark(x1)), MARK(x1)) A__ADD(s(fact(prod(z0, z1))), x1) -> c4(A__ADD(a__fact(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__ADD(s(fact(p(z0))), x1) -> c4(A__ADD(a__fact(a__p(mark(z0))), mark(x1)), MARK(x1)) A__ADD(s(fact(add(z0, z1))), x1) -> c4(A__ADD(a__fact(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__ADD(s(fact(s(z0))), x1) -> c4(A__ADD(a__fact(s(mark(z0))), mark(x1)), MARK(x1)) A__ADD(s(fact(0)), x1) -> c4(A__ADD(a__fact(0), mark(x1)), MARK(x1)) A__ADD(s(fact(true)), x1) -> c4(A__ADD(a__fact(true), mark(x1)), MARK(x1)) A__ADD(s(fact(false)), x1) -> c4(A__ADD(a__fact(false), mark(x1)), MARK(x1)) ---------------------------------------- (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(0), x1) -> c3(A__ADD(0, 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) -> 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-> 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))) 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))) A__ADD(s(x0), s(fact(z0))) -> c4(A__ADD(mark(x0), s(a__fact(mark(z0)))), MARK(s(fact(z0)))) A__ADD(s(x0), s(if(z0, z1, z2))) -> c4(A__ADD(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(s(if(z0, z1, z2)))) A__ADD(s(x0), s(zero(z0))) -> c4(A__ADD(mark(x0), s(a__zero(mark(z0)))), MARK(s(zero(z0)))) A__ADD(s(x0), s(prod(z0, z1))) -> c4(A__ADD(mark(x0), s(a__prod(mark(z0), mark(z1)))), MARK(s(prod(z0, z1)))) A__ADD(s(x0), s(p(z0))) -> c4(A__ADD(mark(x0), s(a__p(mark(z0)))), MARK(s(p(z0)))) A__ADD(s(x0), s(add(z0, z1))) -> c4(A__ADD(mark(x0), s(a__add(mark(z0), mark(z1)))), MARK(s(add(z0, z1)))) A__ADD(s(x0), s(s(z0))) -> c4(A__ADD(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__ADD(s(x0), s(0)) -> c4(A__ADD(mark(x0), s(0)), MARK(s(0))) A__ADD(s(x0), s(true)) -> c4(A__ADD(mark(x0), s(true)), MARK(s(true))) A__ADD(s(x0), s(false)) -> c4(A__ADD(mark(x0), s(false)), MARK(s(false))) A__ADD(s(fact(z0)), s(x1)) -> c4(A__ADD(a__fact(mark(z0)), s(mark(x1))), MARK(s(x1))) A__ADD(s(if(z0, z1, z2)), s(x1)) -> c4(A__ADD(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(s(x1))) A__ADD(s(zero(z0)), s(x1)) -> c4(A__ADD(a__zero(mark(z0)), s(mark(x1))), MARK(s(x1))) A__ADD(s(prod(z0, z1)), s(x1)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__ADD(s(p(z0)), s(x1)) -> c4(A__ADD(a__p(mark(z0)), s(mark(x1))), MARK(s(x1))) A__ADD(s(add(z0, z1)), s(x1)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__ADD(s(s(z0)), s(x1)) -> c4(A__ADD(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__ADD(s(0), s(x1)) -> c4(A__ADD(0, s(mark(x1))), MARK(s(x1))) A__ADD(s(x0), s(x1)) -> c4(MARK(s(x1))) A__ADD(s(true), s(x1)) -> c4(MARK(s(x1))) A__ADD(s(false), s(x1)) -> c4(MARK(s(x1))) A__ADD(s(fact(x0)), 0) -> c4(A__ADD(a__fact(mark(x0)), 0), MARK(0)) A__ADD(s(fact(x0)), true) -> c4(A__ADD(a__fact(mark(x0)), true), MARK(true)) A__ADD(s(fact(x0)), false) -> c4(A__ADD(a__fact(mark(x0)), false), MARK(false)) A__ADD(s(fact(x0)), x1) -> c4(A__ADD(a__if(a__zero(mark(mark(x0))), s(0), prod(mark(x0), fact(p(mark(x0))))), mark(x1)), MARK(x1)) A__ADD(s(fact(x0)), x1) -> c4(A__ADD(fact(mark(x0)), mark(x1)), MARK(x1)) A__ADD(s(fact(fact(z0))), x1) -> c4(A__ADD(a__fact(a__fact(mark(z0))), mark(x1)), MARK(x1)) A__ADD(s(fact(if(z0, z1, z2))), x1) -> c4(A__ADD(a__fact(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__ADD(s(fact(zero(z0))), x1) -> c4(A__ADD(a__fact(a__zero(mark(z0))), mark(x1)), MARK(x1)) A__ADD(s(fact(prod(z0, z1))), x1) -> c4(A__ADD(a__fact(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__ADD(s(fact(p(z0))), x1) -> c4(A__ADD(a__fact(a__p(mark(z0))), mark(x1)), MARK(x1)) A__ADD(s(fact(add(z0, z1))), x1) -> c4(A__ADD(a__fact(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__ADD(s(fact(s(z0))), x1) -> c4(A__ADD(a__fact(s(mark(z0))), mark(x1)), MARK(x1)) A__ADD(s(fact(0)), x1) -> c4(A__ADD(a__fact(0), mark(x1)), MARK(x1)) A__ADD(s(fact(true)), x1) -> c4(A__ADD(a__fact(true), mark(x1)), MARK(x1)) A__ADD(s(fact(false)), x1) -> c4(A__ADD(a__fact(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)) MARK(zero(z0)) -> c21(MARK(z0)) A__ADD(s(0), x1) -> c3(A__ADD(0, 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)))), 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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))), 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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))) A__ADD(s(x0), s(fact(z0))) -> c4(A__ADD(mark(x0), s(a__fact(mark(z0)))), MARK(s(fact(z0)))) A__ADD(s(x0), s(if(z0, z1, z2))) -> c4(A__ADD(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(s(if(z0, z1, z2)))) A__ADD(s(x0), s(zero(z0))) -> c4(A__ADD(mark(x0), s(a__zero(mark(z0)))), MARK(s(zero(z0)))) A__ADD(s(x0), s(prod(z0, z1))) -> c4(A__ADD(mark(x0), s(a__prod(mark(z0), mark(z1)))), MARK(s(prod(z0, z1)))) A__ADD(s(x0), s(p(z0))) -> c4(A__ADD(mark(x0), s(a__p(mark(z0)))), MARK(s(p(z0)))) A__ADD(s(x0), s(add(z0, z1))) -> c4(A__ADD(mark(x0), s(a__add(mark(z0), mark(z1)))), MARK(s(add(z0, z1)))) A__ADD(s(x0), s(s(z0))) -> c4(A__ADD(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__ADD(s(x0), s(0)) -> c4(A__ADD(mark(x0), s(0)), MARK(s(0))) A__ADD(s(x0), s(true)) -> c4(A__ADD(mark(x0), s(true)), MARK(s(true))) A__ADD(s(x0), s(false)) -> c4(A__ADD(mark(x0), s(false)), MARK(s(false))) A__ADD(s(fact(z0)), s(x1)) -> c4(A__ADD(a__fact(mark(z0)), s(mark(x1))), MARK(s(x1))) A__ADD(s(if(z0, z1, z2)), s(x1)) -> c4(A__ADD(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(s(x1))) A__ADD(s(zero(z0)), s(x1)) -> c4(A__ADD(a__zero(mark(z0)), s(mark(x1))), MARK(s(x1))) A__ADD(s(prod(z0, z1)), s(x1)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__ADD(s(p(z0)), s(x1)) -> c4(A__ADD(a__p(mark(z0)), s(mark(x1))), MARK(s(x1))) A__ADD(s(add(z0, z1)), s(x1)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__ADD(s(s(z0)), s(x1)) -> c4(A__ADD(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__ADD(s(0), s(x1)) -> c4(A__ADD(0, s(mark(x1))), MARK(s(x1))) A__ADD(s(x0), s(x1)) -> c4(MARK(s(x1))) A__ADD(s(true), s(x1)) -> c4(MARK(s(x1))) A__ADD(s(false), s(x1)) -> c4(MARK(s(x1))) A__ADD(s(fact(x0)), 0) -> c4(A__ADD(a__fact(mark(x0)), 0), MARK(0)) A__ADD(s(fact(x0)), true) -> c4(A__ADD(a__fact(mark(x0)), true), MARK(true)) A__ADD(s(fact(x0)), false) -> c4(A__ADD(a__fact(mark(x0)), false), MARK(false)) A__ADD(s(fact(x0)), x1) -> c4(A__ADD(a__if(a__zero(mark(mark(x0))), s(0), prod(mark(x0), fact(p(mark(x0))))), mark(x1)), MARK(x1)) A__ADD(s(fact(x0)), x1) -> c4(A__ADD(fact(mark(x0)), mark(x1)), MARK(x1)) A__ADD(s(fact(fact(z0))), x1) -> c4(A__ADD(a__fact(a__fact(mark(z0))), mark(x1)), MARK(x1)) A__ADD(s(fact(if(z0, z1, z2))), x1) -> c4(A__ADD(a__fact(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__ADD(s(fact(zero(z0))), x1) -> c4(A__ADD(a__fact(a__zero(mark(z0))), mark(x1)), MARK(x1)) A__ADD(s(fact(prod(z0, z1))), x1) -> c4(A__ADD(a__fact(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__ADD(s(fact(p(z0))), x1) -> c4(A__ADD(a__fact(a__p(mark(z0))), mark(x1)), MARK(x1)) A__ADD(s(fact(add(z0, z1))), x1) -> c4(A__ADD(a__fact(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__ADD(s(fact(s(z0))), x1) -> c4(A__ADD(a__fact(s(mark(z0))), mark(x1)), MARK(x1)) A__ADD(s(fact(0)), x1) -> c4(A__ADD(a__fact(0), mark(x1)), MARK(x1)) A__ADD(s(fact(true)), x1) -> c4(A__ADD(a__fact(true), mark(x1)), MARK(x1)) A__ADD(s(fact(false)), x1) -> c4(A__ADD(a__fact(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__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 ---------------------------------------- (201) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (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(0), x1) -> c3(A__ADD(0, 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))))), 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-> 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))) 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))) A__ADD(s(x0), s(fact(z0))) -> c4(A__ADD(mark(x0), s(a__fact(mark(z0)))), MARK(s(fact(z0)))) A__ADD(s(x0), s(if(z0, z1, z2))) -> c4(A__ADD(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(s(if(z0, z1, z2)))) A__ADD(s(x0), s(zero(z0))) -> c4(A__ADD(mark(x0), s(a__zero(mark(z0)))), MARK(s(zero(z0)))) A__ADD(s(x0), s(prod(z0, z1))) -> c4(A__ADD(mark(x0), s(a__prod(mark(z0), mark(z1)))), MARK(s(prod(z0, z1)))) A__ADD(s(x0), s(p(z0))) -> c4(A__ADD(mark(x0), s(a__p(mark(z0)))), MARK(s(p(z0)))) A__ADD(s(x0), s(add(z0, z1))) -> c4(A__ADD(mark(x0), s(a__add(mark(z0), mark(z1)))), MARK(s(add(z0, z1)))) A__ADD(s(x0), s(s(z0))) -> c4(A__ADD(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__ADD(s(x0), s(0)) -> c4(A__ADD(mark(x0), s(0)), MARK(s(0))) A__ADD(s(x0), s(true)) -> c4(A__ADD(mark(x0), s(true)), MARK(s(true))) A__ADD(s(x0), s(false)) -> c4(A__ADD(mark(x0), s(false)), MARK(s(false))) A__ADD(s(fact(z0)), s(x1)) -> c4(A__ADD(a__fact(mark(z0)), s(mark(x1))), MARK(s(x1))) A__ADD(s(if(z0, z1, z2)), s(x1)) -> c4(A__ADD(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(s(x1))) A__ADD(s(zero(z0)), s(x1)) -> c4(A__ADD(a__zero(mark(z0)), s(mark(x1))), MARK(s(x1))) A__ADD(s(prod(z0, z1)), s(x1)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__ADD(s(p(z0)), s(x1)) -> c4(A__ADD(a__p(mark(z0)), s(mark(x1))), MARK(s(x1))) A__ADD(s(add(z0, z1)), s(x1)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__ADD(s(s(z0)), s(x1)) -> c4(A__ADD(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__ADD(s(0), s(x1)) -> c4(A__ADD(0, s(mark(x1))), MARK(s(x1))) A__ADD(s(x0), s(x1)) -> c4(MARK(s(x1))) A__ADD(s(true), s(x1)) -> c4(MARK(s(x1))) A__ADD(s(false), s(x1)) -> c4(MARK(s(x1))) A__ADD(s(fact(x0)), x1) -> c4(A__ADD(a__if(a__zero(mark(mark(x0))), s(0), prod(mark(x0), fact(p(mark(x0))))), mark(x1)), MARK(x1)) A__ADD(s(fact(fact(z0))), x1) -> c4(A__ADD(a__fact(a__fact(mark(z0))), mark(x1)), MARK(x1)) A__ADD(s(fact(if(z0, z1, z2))), x1) -> c4(A__ADD(a__fact(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__ADD(s(fact(zero(z0))), x1) -> c4(A__ADD(a__fact(a__zero(mark(z0))), mark(x1)), MARK(x1)) A__ADD(s(fact(prod(z0, z1))), x1) -> c4(A__ADD(a__fact(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__ADD(s(fact(p(z0))), x1) -> c4(A__ADD(a__fact(a__p(mark(z0))), mark(x1)), MARK(x1)) A__ADD(s(fact(add(z0, z1))), x1) -> c4(A__ADD(a__fact(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__ADD(s(fact(s(z0))), x1) -> c4(A__ADD(a__fact(s(mark(z0))), mark(x1)), MARK(x1)) A__ADD(s(fact(0)), x1) -> c4(A__ADD(a__fact(0), mark(x1)), MARK(x1)) A__ADD(s(fact(true)), x1) -> c4(A__ADD(a__fact(true), mark(x1)), MARK(x1)) A__ADD(s(fact(false)), x1) -> c4(A__ADD(a__fact(false), mark(x1)), MARK(x1)) A__ADD(s(fact(x0)), 0) -> c4(A__ADD(a__fact(mark(x0)), 0)) A__ADD(s(fact(x0)), true) -> c4(A__ADD(a__fact(mark(x0)), true)) A__ADD(s(fact(x0)), false) -> c4(A__ADD(a__fact(mark(x0)), false)) A__ADD(s(fact(x0)), x1) -> c4(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(0), x1) -> c3(A__ADD(0, 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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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))) 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))) A__ADD(s(x0), s(fact(z0))) -> c4(A__ADD(mark(x0), s(a__fact(mark(z0)))), MARK(s(fact(z0)))) A__ADD(s(x0), s(if(z0, z1, z2))) -> c4(A__ADD(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(s(if(z0, z1, z2)))) A__ADD(s(x0), s(zero(z0))) -> c4(A__ADD(mark(x0), s(a__zero(mark(z0)))), MARK(s(zero(z0)))) A__ADD(s(x0), s(prod(z0, z1))) -> c4(A__ADD(mark(x0), s(a__prod(mark(z0), mark(z1)))), MARK(s(prod(z0, z1)))) A__ADD(s(x0), s(p(z0))) -> c4(A__ADD(mark(x0), s(a__p(mark(z0)))), MARK(s(p(z0)))) A__ADD(s(x0), s(add(z0, z1))) -> c4(A__ADD(mark(x0), s(a__add(mark(z0), mark(z1)))), MARK(s(add(z0, z1)))) A__ADD(s(x0), s(s(z0))) -> c4(A__ADD(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__ADD(s(x0), s(0)) -> c4(A__ADD(mark(x0), s(0)), MARK(s(0))) A__ADD(s(x0), s(true)) -> c4(A__ADD(mark(x0), s(true)), MARK(s(true))) A__ADD(s(x0), s(false)) -> c4(A__ADD(mark(x0), s(false)), MARK(s(false))) A__ADD(s(fact(z0)), s(x1)) -> c4(A__ADD(a__fact(mark(z0)), s(mark(x1))), MARK(s(x1))) A__ADD(s(if(z0, z1, z2)), s(x1)) -> c4(A__ADD(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(s(x1))) A__ADD(s(zero(z0)), s(x1)) -> c4(A__ADD(a__zero(mark(z0)), s(mark(x1))), MARK(s(x1))) A__ADD(s(prod(z0, z1)), s(x1)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__ADD(s(p(z0)), s(x1)) -> c4(A__ADD(a__p(mark(z0)), s(mark(x1))), MARK(s(x1))) A__ADD(s(add(z0, z1)), s(x1)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__ADD(s(s(z0)), s(x1)) -> c4(A__ADD(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__ADD(s(0), s(x1)) -> c4(A__ADD(0, s(mark(x1))), MARK(s(x1))) A__ADD(s(x0), s(x1)) -> c4(MARK(s(x1))) A__ADD(s(true), s(x1)) -> c4(MARK(s(x1))) A__ADD(s(false), s(x1)) -> c4(MARK(s(x1))) A__ADD(s(fact(x0)), x1) -> c4(A__ADD(a__if(a__zero(mark(mark(x0))), s(0), prod(mark(x0), fact(p(mark(x0))))), mark(x1)), MARK(x1)) A__ADD(s(fact(fact(z0))), x1) -> c4(A__ADD(a__fact(a__fact(mark(z0))), mark(x1)), MARK(x1)) A__ADD(s(fact(if(z0, z1, z2))), x1) -> c4(A__ADD(a__fact(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__ADD(s(fact(zero(z0))), x1) -> c4(A__ADD(a__fact(a__zero(mark(z0))), mark(x1)), MARK(x1)) A__ADD(s(fact(prod(z0, z1))), x1) -> c4(A__ADD(a__fact(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__ADD(s(fact(p(z0))), x1) -> c4(A__ADD(a__fact(a__p(mark(z0))), mark(x1)), MARK(x1)) A__ADD(s(fact(add(z0, z1))), x1) -> c4(A__ADD(a__fact(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__ADD(s(fact(s(z0))), x1) -> c4(A__ADD(a__fact(s(mark(z0))), mark(x1)), MARK(x1)) A__ADD(s(fact(0)), x1) -> c4(A__ADD(a__fact(0), mark(x1)), MARK(x1)) A__ADD(s(fact(true)), x1) -> c4(A__ADD(a__fact(true), mark(x1)), MARK(x1)) A__ADD(s(fact(false)), x1) -> c4(A__ADD(a__fact(false), mark(x1)), MARK(x1)) A__ADD(s(fact(x0)), 0) -> c4(A__ADD(a__fact(mark(x0)), 0)) A__ADD(s(fact(x0)), true) -> c4(A__ADD(a__fact(mark(x0)), true)) A__ADD(s(fact(x0)), false) -> c4(A__ADD(a__fact(mark(x0)), false)) A__ADD(s(fact(x0)), 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__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 ---------------------------------------- (203) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__ADD(s(if(z0, z1, z2)), x1) -> c4(A__ADD(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) by A__ADD(s(if(x0, x1, x2)), fact(z0)) -> c4(A__ADD(a__if(mark(x0), x1, x2), a__fact(mark(z0))), MARK(fact(z0))) A__ADD(s(if(x0, x1, x2)), if(z0, z1, z2)) -> c4(A__ADD(a__if(mark(x0), x1, x2), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) A__ADD(s(if(x0, x1, x2)), zero(z0)) -> c4(A__ADD(a__if(mark(x0), x1, x2), a__zero(mark(z0))), MARK(zero(z0))) A__ADD(s(if(x0, x1, x2)), prod(z0, z1)) -> c4(A__ADD(a__if(mark(x0), x1, x2), a__prod(mark(z0), mark(z1))), MARK(prod(z0, z1))) A__ADD(s(if(x0, x1, x2)), p(z0)) -> c4(A__ADD(a__if(mark(x0), x1, x2), a__p(mark(z0))), MARK(p(z0))) A__ADD(s(if(x0, x1, x2)), add(z0, z1)) -> c4(A__ADD(a__if(mark(x0), x1, x2), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(if(x0, x1, x2)), s(z0)) -> c4(A__ADD(a__if(mark(x0), x1, x2), s(mark(z0))), MARK(s(z0))) A__ADD(s(if(x0, x1, x2)), 0) -> c4(A__ADD(a__if(mark(x0), x1, x2), 0), MARK(0)) A__ADD(s(if(x0, x1, x2)), true) -> c4(A__ADD(a__if(mark(x0), x1, x2), true), MARK(true)) A__ADD(s(if(x0, x1, x2)), false) -> c4(A__ADD(a__if(mark(x0), x1, x2), false), MARK(false)) A__ADD(s(if(x0, z1, z2)), x3) -> c4(A__ADD(if(mark(x0), z1, z2), mark(x3)), MARK(x3)) A__ADD(s(if(fact(z0), x1, x2)), x3) -> c4(A__ADD(a__if(a__fact(mark(z0)), x1, x2), mark(x3)), MARK(x3)) A__ADD(s(if(if(z0, z1, z2), x1, x2)), x3) -> c4(A__ADD(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3)) A__ADD(s(if(zero(z0), x1, x2)), x3) -> c4(A__ADD(a__if(a__zero(mark(z0)), x1, x2), mark(x3)), MARK(x3)) A__ADD(s(if(prod(z0, z1), x1, x2)), x3) -> c4(A__ADD(a__if(a__prod(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3)) A__ADD(s(if(p(z0), x1, x2)), x3) -> c4(A__ADD(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(x3)) A__ADD(s(if(add(z0, z1), x1, x2)), x3) -> c4(A__ADD(a__if(a__add(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3)) A__ADD(s(if(s(z0), x1, x2)), x3) -> c4(A__ADD(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(x3)) A__ADD(s(if(0, x1, x2)), x3) -> c4(A__ADD(a__if(0, x1, x2), mark(x3)), MARK(x3)) A__ADD(s(if(true, x1, x2)), x3) -> c4(A__ADD(a__if(true, x1, x2), mark(x3)), MARK(x3)) A__ADD(s(if(false, x1, x2)), x3) -> c4(A__ADD(a__if(false, x1, x2), mark(x3)), MARK(x3)) ---------------------------------------- (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(0), x1) -> c3(A__ADD(0, 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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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)) 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s(fact(z0))) -> c4(A__ADD(mark(x0), s(a__fact(mark(z0)))), MARK(s(fact(z0)))) A__ADD(s(x0), s(if(z0, z1, z2))) -> c4(A__ADD(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(s(if(z0, z1, z2)))) A__ADD(s(x0), s(zero(z0))) -> c4(A__ADD(mark(x0), s(a__zero(mark(z0)))), MARK(s(zero(z0)))) A__ADD(s(x0), s(prod(z0, z1))) -> c4(A__ADD(mark(x0), s(a__prod(mark(z0), mark(z1)))), MARK(s(prod(z0, z1)))) A__ADD(s(x0), s(p(z0))) -> c4(A__ADD(mark(x0), s(a__p(mark(z0)))), MARK(s(p(z0)))) A__ADD(s(x0), s(add(z0, z1))) -> c4(A__ADD(mark(x0), s(a__add(mark(z0), mark(z1)))), MARK(s(add(z0, z1)))) A__ADD(s(x0), s(s(z0))) -> c4(A__ADD(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__ADD(s(x0), s(0)) -> c4(A__ADD(mark(x0), s(0)), MARK(s(0))) A__ADD(s(x0), s(true)) -> c4(A__ADD(mark(x0), s(true)), MARK(s(true))) A__ADD(s(x0), s(false)) -> c4(A__ADD(mark(x0), s(false)), MARK(s(false))) A__ADD(s(fact(z0)), s(x1)) -> c4(A__ADD(a__fact(mark(z0)), s(mark(x1))), MARK(s(x1))) A__ADD(s(if(z0, z1, z2)), s(x1)) -> c4(A__ADD(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(s(x1))) A__ADD(s(zero(z0)), s(x1)) -> c4(A__ADD(a__zero(mark(z0)), s(mark(x1))), MARK(s(x1))) A__ADD(s(prod(z0, z1)), s(x1)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__ADD(s(p(z0)), s(x1)) -> c4(A__ADD(a__p(mark(z0)), s(mark(x1))), MARK(s(x1))) A__ADD(s(add(z0, z1)), s(x1)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__ADD(s(s(z0)), s(x1)) -> c4(A__ADD(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__ADD(s(0), s(x1)) -> c4(A__ADD(0, s(mark(x1))), MARK(s(x1))) A__ADD(s(x0), s(x1)) -> c4(MARK(s(x1))) A__ADD(s(true), s(x1)) -> c4(MARK(s(x1))) A__ADD(s(false), s(x1)) -> c4(MARK(s(x1))) A__ADD(s(fact(x0)), x1) -> c4(A__ADD(a__if(a__zero(mark(mark(x0))), s(0), prod(mark(x0), fact(p(mark(x0))))), mark(x1)), MARK(x1)) A__ADD(s(fact(fact(z0))), x1) -> c4(A__ADD(a__fact(a__fact(mark(z0))), mark(x1)), MARK(x1)) A__ADD(s(fact(if(z0, z1, z2))), x1) -> c4(A__ADD(a__fact(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__ADD(s(fact(zero(z0))), x1) -> c4(A__ADD(a__fact(a__zero(mark(z0))), mark(x1)), MARK(x1)) A__ADD(s(fact(prod(z0, z1))), x1) -> c4(A__ADD(a__fact(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__ADD(s(fact(p(z0))), x1) -> c4(A__ADD(a__fact(a__p(mark(z0))), mark(x1)), MARK(x1)) A__ADD(s(fact(add(z0, z1))), x1) -> c4(A__ADD(a__fact(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__ADD(s(fact(s(z0))), x1) -> c4(A__ADD(a__fact(s(mark(z0))), mark(x1)), MARK(x1)) A__ADD(s(fact(0)), x1) -> c4(A__ADD(a__fact(0), mark(x1)), MARK(x1)) A__ADD(s(fact(true)), x1) -> c4(A__ADD(a__fact(true), mark(x1)), MARK(x1)) A__ADD(s(fact(false)), x1) -> c4(A__ADD(a__fact(false), mark(x1)), MARK(x1)) A__ADD(s(fact(x0)), 0) -> c4(A__ADD(a__fact(mark(x0)), 0)) A__ADD(s(fact(x0)), true) -> c4(A__ADD(a__fact(mark(x0)), true)) A__ADD(s(fact(x0)), false) -> c4(A__ADD(a__fact(mark(x0)), false)) A__ADD(s(fact(x0)), x1) -> c4(MARK(x1)) A__ADD(s(if(x0, x1, x2)), 0) -> c4(A__ADD(a__if(mark(x0), x1, x2), 0), MARK(0)) A__ADD(s(if(x0, x1, x2)), true) -> c4(A__ADD(a__if(mark(x0), x1, x2), true), MARK(true)) A__ADD(s(if(x0, x1, x2)), false) -> c4(A__ADD(a__if(mark(x0), x1, x2), false), MARK(false)) A__ADD(s(if(x0, z1, z2)), x3) -> c4(A__ADD(if(mark(x0), z1, z2), mark(x3)), MARK(x3)) A__ADD(s(if(fact(z0), x1, x2)), x3) -> c4(A__ADD(a__if(a__fact(mark(z0)), x1, x2), mark(x3)), MARK(x3)) A__ADD(s(if(if(z0, z1, z2), x1, x2)), x3) -> c4(A__ADD(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3)) A__ADD(s(if(zero(z0), x1, x2)), x3) -> c4(A__ADD(a__if(a__zero(mark(z0)), x1, x2), mark(x3)), MARK(x3)) A__ADD(s(if(prod(z0, z1), x1, x2)), x3) -> c4(A__ADD(a__if(a__prod(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3)) A__ADD(s(if(p(z0), x1, x2)), x3) -> c4(A__ADD(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(x3)) A__ADD(s(if(add(z0, z1), x1, x2)), x3) -> c4(A__ADD(a__if(a__add(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3)) A__ADD(s(if(s(z0), x1, x2)), x3) -> c4(A__ADD(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(x3)) A__ADD(s(if(0, x1, x2)), x3) -> c4(A__ADD(a__if(0, x1, x2), mark(x3)), MARK(x3)) A__ADD(s(if(true, x1, x2)), x3) -> c4(A__ADD(a__if(true, x1, x2), mark(x3)), MARK(x3)) A__ADD(s(if(false, x1, x2)), x3) -> c4(A__ADD(a__if(false, x1, x2), mark(x3)), 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(0), x1) -> c3(A__ADD(0, 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), 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)) -> 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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))) 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))) 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))) A__ADD(s(x0), s(fact(z0))) -> c4(A__ADD(mark(x0), s(a__fact(mark(z0)))), MARK(s(fact(z0)))) A__ADD(s(x0), s(if(z0, z1, z2))) -> c4(A__ADD(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(s(if(z0, z1, z2)))) A__ADD(s(x0), s(zero(z0))) -> c4(A__ADD(mark(x0), s(a__zero(mark(z0)))), MARK(s(zero(z0)))) A__ADD(s(x0), s(prod(z0, z1))) -> c4(A__ADD(mark(x0), s(a__prod(mark(z0), mark(z1)))), MARK(s(prod(z0, z1)))) A__ADD(s(x0), s(p(z0))) -> c4(A__ADD(mark(x0), s(a__p(mark(z0)))), MARK(s(p(z0)))) A__ADD(s(x0), s(add(z0, z1))) -> c4(A__ADD(mark(x0), s(a__add(mark(z0), mark(z1)))), MARK(s(add(z0, z1)))) A__ADD(s(x0), s(s(z0))) -> c4(A__ADD(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__ADD(s(x0), s(0)) -> c4(A__ADD(mark(x0), s(0)), MARK(s(0))) A__ADD(s(x0), s(true)) -> c4(A__ADD(mark(x0), s(true)), MARK(s(true))) A__ADD(s(x0), s(false)) -> c4(A__ADD(mark(x0), s(false)), MARK(s(false))) A__ADD(s(fact(z0)), s(x1)) -> c4(A__ADD(a__fact(mark(z0)), s(mark(x1))), MARK(s(x1))) A__ADD(s(if(z0, z1, z2)), s(x1)) -> c4(A__ADD(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(s(x1))) A__ADD(s(zero(z0)), s(x1)) -> c4(A__ADD(a__zero(mark(z0)), s(mark(x1))), MARK(s(x1))) A__ADD(s(prod(z0, z1)), s(x1)) -> c4(A__ADD(a__prod(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__ADD(s(p(z0)), s(x1)) -> c4(A__ADD(a__p(mark(z0)), s(mark(x1))), MARK(s(x1))) A__ADD(s(add(z0, z1)), s(x1)) -> c4(A__ADD(a__add(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__ADD(s(s(z0)), s(x1)) -> c4(A__ADD(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__ADD(s(0), s(x1)) -> c4(A__ADD(0, s(mark(x1))), MARK(s(x1))) A__ADD(s(x0), s(x1)) -> c4(MARK(s(x1))) A__ADD(s(true), s(x1)) -> c4(MARK(s(x1))) A__ADD(s(false), s(x1)) -> c4(MARK(s(x1))) A__ADD(s(fact(x0)), x1) -> c4(A__ADD(a__if(a__zero(mark(mark(x0))), s(0), prod(mark(x0), fact(p(mark(x0))))), mark(x1)), MARK(x1)) A__ADD(s(fact(fact(z0))), x1) -> c4(A__ADD(a__fact(a__fact(mark(z0))), mark(x1)), MARK(x1)) A__ADD(s(fact(if(z0, z1, z2))), x1) -> c4(A__ADD(a__fact(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__ADD(s(fact(zero(z0))), x1) -> c4(A__ADD(a__fact(a__zero(mark(z0))), mark(x1)), MARK(x1)) A__ADD(s(fact(prod(z0, z1))), x1) -> c4(A__ADD(a__fact(a__prod(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__ADD(s(fact(p(z0))), x1) -> c4(A__ADD(a__fact(a__p(mark(z0))), mark(x1)), MARK(x1)) A__ADD(s(fact(add(z0, z1))), x1) -> c4(A__ADD(a__fact(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__ADD(s(fact(s(z0))), x1) -> c4(A__ADD(a__fact(s(mark(z0))), mark(x1)), MARK(x1)) A__ADD(s(fact(0)), x1) -> c4(A__ADD(a__fact(0), mark(x1)), MARK(x1)) A__ADD(s(fact(true)), x1) -> c4(A__ADD(a__fact(true), mark(x1)), MARK(x1)) A__ADD(s(fact(false)), x1) -> c4(A__ADD(a__fact(false), mark(x1)), MARK(x1)) A__ADD(s(fact(x0)), 0) -> c4(A__ADD(a__fact(mark(x0)), 0)) A__ADD(s(fact(x0)), true) -> c4(A__ADD(a__fact(mark(x0)), true)) A__ADD(s(fact(x0)), false) -> c4(A__ADD(a__fact(mark(x0)), false)) A__ADD(s(fact(x0)), x1) -> c4(MARK(x1)) A__ADD(s(if(x0, x1, x2)), 0) -> c4(A__ADD(a__if(mark(x0), x1, x2), 0), MARK(0)) A__ADD(s(if(x0, x1, x2)), true) -> c4(A__ADD(a__if(mark(x0), x1, x2), true), MARK(true)) A__ADD(s(if(x0, x1, x2)), false) -> c4(A__ADD(a__if(mark(x0), x1, x2), false), MARK(false)) A__ADD(s(if(x0, z1, z2)), x3) -> c4(A__ADD(if(mark(x0), z1, z2), mark(x3)), MARK(x3)) A__ADD(s(if(fact(z0), x1, x2)), x3) -> c4(A__ADD(a__if(a__fact(mark(z0)), x1, x2), mark(x3)), MARK(x3)) A__ADD(s(if(if(z0, z1, z2), x1, x2)), x3) -> c4(A__ADD(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3)) A__ADD(s(if(zero(z0), x1, x2)), x3) -> c4(A__ADD(a__if(a__zero(mark(z0)), x1, x2), mark(x3)), MARK(x3)) A__ADD(s(if(prod(z0, z1), x1, x2)), x3) -> c4(A__ADD(a__if(a__prod(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3)) A__ADD(s(if(p(z0), x1, x2)), x3) -> c4(A__ADD(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(x3)) A__ADD(s(if(add(z0, z1), x1, x2)), x3) -> c4(A__ADD(a__if(a__add(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3)) A__ADD(s(if(s(z0), x1, x2)), x3) -> c4(A__ADD(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(x3)) A__ADD(s(if(0, x1, x2)), x3) -> c4(A__ADD(a__if(0, x1, x2), mark(x3)), MARK(x3)) A__ADD(s(if(true, x1, x2)), x3) -> c4(A__ADD(a__if(true, x1, x2), mark(x3)), MARK(x3)) A__ADD(s(if(false, x1, x2)), x3) -> c4(A__ADD(a__if(false, x1, x2), mark(x3)), 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_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